---
OA_place: repository
OA_type: green
_id: '20155'
abstract:
- lang: eng
text: We study time averages for the norm of solutions to kinetic Fokker–Planck
equations associated with general Hamiltonians. We provide fully explicit and
constructive decay estimates for systems subject to a confining potential, allowing
fat-tail, subexponential and (super-)exponential local equilibria, which also
include the classic Maxwellian case. The key step in our estimates is a modified
Poincaré inequality, obtained via a Lions–Poincaré inequality and an averaging
lemma.
acknowledgement: The first author was funded by the European Union's Horizon 2020
research andinnovation program under the Marie Sklodowska-Curie grant agreements
754362 and 101034413,and partially by Project EFI (ANR-17-CE40-0030) of the French
National Research Agency (ANR).The work of the second author was partially funded
by the European Research Council (ERC) underthe European Union's Horizon 2020 research
and innovation programme (grant agreement 810367),and by the Agence Nationale de
la Recherche under grants ANR-19-CE40-0010 (QuAMProcs) andANR-21-CE40-0006 (SINEQ).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giovanni
full_name: Brigati, Giovanni
id: 63ff57e8-1fbb-11ee-88f2-f558ffc59cf1
last_name: Brigati
- first_name: Gabriel
full_name: Stoltz, Gabriel
last_name: Stoltz
citation:
ama: Brigati G, Stoltz G. How to construct explicit decay rates for kinetic Fokker–Planck
equations? SIAM Journal on Mathematical Analysis. 2025;57(4):3587-3622.
doi:10.1137/24M1700351
apa: Brigati, G., & Stoltz, G. (2025). How to construct explicit decay rates
for kinetic Fokker–Planck equations? SIAM Journal on Mathematical Analysis.
Society for Industrial and Applied Mathematics. https://doi.org/10.1137/24M1700351
chicago: Brigati, Giovanni, and Gabriel Stoltz. “How to Construct Explicit Decay
Rates for Kinetic Fokker–Planck Equations?” SIAM Journal on Mathematical Analysis.
Society for Industrial and Applied Mathematics, 2025. https://doi.org/10.1137/24M1700351.
ieee: G. Brigati and G. Stoltz, “How to construct explicit decay rates for kinetic
Fokker–Planck equations?,” SIAM Journal on Mathematical Analysis, vol.
57, no. 4. Society for Industrial and Applied Mathematics, pp. 3587–3622, 2025.
ista: Brigati G, Stoltz G. 2025. How to construct explicit decay rates for kinetic
Fokker–Planck equations? SIAM Journal on Mathematical Analysis. 57(4), 3587–3622.
mla: Brigati, Giovanni, and Gabriel Stoltz. “How to Construct Explicit Decay Rates
for Kinetic Fokker–Planck Equations?” SIAM Journal on Mathematical Analysis,
vol. 57, no. 4, Society for Industrial and Applied Mathematics, 2025, pp. 3587–622,
doi:10.1137/24M1700351.
short: G. Brigati, G. Stoltz, SIAM Journal on Mathematical Analysis 57 (2025) 3587–3622.
corr_author: '1'
date_created: 2025-08-10T22:01:29Z
date_published: 2025-08-01T00:00:00Z
date_updated: 2025-11-05T13:51:40Z
day: '01'
department:
- _id: JaMa
doi: 10.1137/24M1700351
ec_funded: 1
external_id:
arxiv:
- '2302.14506'
isi:
- '001550830900006'
intvolume: ' 57'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2302.14506
month: '08'
oa: 1
oa_version: Preprint
page: 3587-3622
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- 1095-7154
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: How to construct explicit decay rates for kinetic Fokker–Planck equations?
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 57
year: '2025'
...
---
_id: '17372'
abstract:
- lang: eng
text: 'In this paper, we investigate the global well-posedness of reaction-diffusion
systems with transport noise on the d-dimensional torus. We show new global well-posedness
results for a large class of scalar equations (e.g. the Allen-Cahn equation),
and dissipative systems (e.g. equations in coagulation dynamics). Moreover, we
prove global well-posedness for two weakly dissipative systems: Lotka-Volterra
equations for d∈{1,2,3,4} and the Brusselator for d∈{1,2,3}. Many of the results
are also new without transport noise. The proofs are based on maximal regularity
techniques, positivity results, and sharp blow-up criteria developed in our recent
works, combined with energy estimates based on Itô''s formula and stochastic Gronwall
inequalities. Key novelties include the introduction of new Lζ -coercivity/dissipativity
conditions and the development of an Lp(Lq) -framework for systems of reaction-diffusion
equations, which are needed when treating dimensions d∈{2,3} in the case of
cubic or higher order nonlinearities.'
acknowledgement: The first author’s research was supported by the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
grant 948819. . The second author’s research was supported by the VICI subsidy VI.C.212.027
of the Netherlands Organisation for Scientific Research (NWO).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Mark
full_name: Veraar, Mark
last_name: Veraar
citation:
ama: 'Agresti A, Veraar M. Reaction-diffusion equations with transport noise and
critical superlinear diffusion: Global well-posedness of weakly dissipative systems.
SIAM Journal on Mathematical Analysis. 2024;56(4):4870-4927. doi:10.1137/23M1562482'
apa: 'Agresti, A., & Veraar, M. (2024). Reaction-diffusion equations with transport
noise and critical superlinear diffusion: Global well-posedness of weakly dissipative
systems. SIAM Journal on Mathematical Analysis. Society for Industrial
and Applied Mathematics. https://doi.org/10.1137/23M1562482'
chicago: 'Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with
Transport Noise and Critical Superlinear Diffusion: Global Well-Posedness of Weakly
Dissipative Systems.” SIAM Journal on Mathematical Analysis. Society for
Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/23M1562482.'
ieee: 'A. Agresti and M. Veraar, “Reaction-diffusion equations with transport noise
and critical superlinear diffusion: Global well-posedness of weakly dissipative
systems,” SIAM Journal on Mathematical Analysis, vol. 56, no. 4. Society
for Industrial and Applied Mathematics, pp. 4870–4927, 2024.'
ista: 'Agresti A, Veraar M. 2024. Reaction-diffusion equations with transport noise
and critical superlinear diffusion: Global well-posedness of weakly dissipative
systems. SIAM Journal on Mathematical Analysis. 56(4), 4870–4927.'
mla: 'Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport
Noise and Critical Superlinear Diffusion: Global Well-Posedness of Weakly Dissipative
Systems.” SIAM Journal on Mathematical Analysis, vol. 56, no. 4, Society
for Industrial and Applied Mathematics, 2024, pp. 4870–927, doi:10.1137/23M1562482.'
short: A. Agresti, M. Veraar, SIAM Journal on Mathematical Analysis 56 (2024) 4870–4927.
corr_author: '1'
date_created: 2024-08-04T22:01:21Z
date_published: 2024-08-01T00:00:00Z
date_updated: 2025-09-08T08:46:57Z
day: '01'
department:
- _id: JuFi
doi: 10.1137/23M1562482
ec_funded: 1
external_id:
arxiv:
- '2301.06897'
isi:
- '001315424500021'
intvolume: ' 56'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2301.06897
month: '08'
oa: 1
oa_version: Preprint
page: 4870-4927
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- 1095-7154
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Reaction-diffusion equations with transport noise and critical superlinear
diffusion: Global well-posedness of weakly dissipative systems'
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 56
year: '2024'
...
---
_id: '11739'
abstract:
- lang: eng
text: We consider finite-volume approximations of Fokker--Planck equations on bounded
convex domains in $\mathbb{R}^d$ and study the corresponding gradient flow structures.
We reprove the convergence of the discrete to continuous Fokker--Planck equation
via the method of evolutionary $\Gamma$-convergence, i.e., we pass to the limit
at the level of the gradient flow structures, generalizing the one-dimensional
result obtained by Disser and Liero. The proof is of variational nature and relies
on a Mosco convergence result for functionals in the discrete-to-continuum limit
that is of independent interest. Our results apply to arbitrary regular meshes,
even though the associated discrete transport distances may fail to converge to
the Wasserstein distance in this generality.
acknowledgement: This work was supported by the European Research Council (ERC) under
the European Union's Horizon 2020 Research and Innovation Programme grant 716117
and by the AustrianScience Fund (FWF) through grants F65 and W1245.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Dominik L
full_name: Forkert, Dominik L
id: 35C79D68-F248-11E8-B48F-1D18A9856A87
last_name: Forkert
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
citation:
ama: Forkert DL, Maas J, Portinale L. Evolutionary $\Gamma$-convergence of entropic
gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM
Journal on Mathematical Analysis. 2022;54(4):4297-4333. doi:10.1137/21M1410968
apa: Forkert, D. L., Maas, J., & Portinale, L. (2022). Evolutionary $\Gamma$-convergence
of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions.
SIAM Journal on Mathematical Analysis. Society for Industrial and Applied
Mathematics. https://doi.org/10.1137/21M1410968
chicago: Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary $\Gamma$-Convergence
of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.”
SIAM Journal on Mathematical Analysis. Society for Industrial and Applied
Mathematics, 2022. https://doi.org/10.1137/21M1410968.
ieee: D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary $\Gamma$-convergence
of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions,”
SIAM Journal on Mathematical Analysis, vol. 54, no. 4. Society for Industrial
and Applied Mathematics, pp. 4297–4333, 2022.
ista: Forkert DL, Maas J, Portinale L. 2022. Evolutionary $\Gamma$-convergence of
entropic gradient flow structures for Fokker-Planck equations in multiple dimensions.
SIAM Journal on Mathematical Analysis. 54(4), 4297–4333.
mla: Forkert, Dominik L., et al. “Evolutionary $\Gamma$-Convergence of Entropic
Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.”
SIAM Journal on Mathematical Analysis, vol. 54, no. 4, Society for Industrial
and Applied Mathematics, 2022, pp. 4297–333, doi:10.1137/21M1410968.
short: D.L. Forkert, J. Maas, L. Portinale, SIAM Journal on Mathematical Analysis
54 (2022) 4297–4333.
corr_author: '1'
date_created: 2022-08-07T22:01:59Z
date_published: 2022-07-18T00:00:00Z
date_updated: 2025-04-15T08:31:31Z
day: '18'
department:
- _id: JaMa
doi: 10.1137/21M1410968
ec_funded: 1
external_id:
arxiv:
- '2008.10962'
isi:
- '000889274600001'
intvolume: ' 54'
isi: 1
issue: '4'
keyword:
- Fokker--Planck equation
- gradient flow
- evolutionary $\Gamma$-convergence
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2008.10962'
month: '07'
oa: 1
oa_version: Preprint
page: 4297-4333
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 260788DE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: W1245
name: Dissipation and dispersion in nonlinear partial differential equations
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- 1095-7154
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
related_material:
record:
- id: '10022'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Evolutionary $\Gamma$-convergence of entropic gradient flow structures for
Fokker-Planck equations in multiple dimensions
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 54
year: '2022'
...
---
_id: '12305'
abstract:
- lang: eng
text: This paper is concerned with the sharp interface limit for the Allen--Cahn
equation with a nonlinear Robin boundary condition in a bounded smooth domain
Ω⊂\R2. We assume that a diffuse interface already has developed and that it is
in contact with the boundary ∂Ω. The boundary condition is designed in such a
way that the limit problem is given by the mean curvature flow with constant α-contact
angle. For α close to 90° we prove a local in time convergence result for well-prepared
initial data for times when a smooth solution to the limit problem exists. Based
on the latter we construct a suitable curvilinear coordinate system and carry
out a rigorous asymptotic expansion for the Allen--Cahn equation with the nonlinear
Robin boundary condition. Moreover, we show a spectral estimate for the corresponding
linearized Allen--Cahn operator and with its aid we derive strong norm estimates
for the difference of the exact and approximate solutions using a Gronwall-type
argument.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Helmut
full_name: Abels, Helmut
last_name: Abels
- first_name: Maximilian
full_name: Moser, Maximilian
id: a60047a9-da77-11eb-85b4-c4dc385ebb8c
last_name: Moser
citation:
ama: Abels H, Moser M. Convergence of the Allen--Cahn equation with a nonlinear
Robin boundary condition to mean curvature flow with contact angle close to 90°.
SIAM Journal on Mathematical Analysis. 2022;54(1):114-172. doi:10.1137/21m1424925
apa: Abels, H., & Moser, M. (2022). Convergence of the Allen--Cahn equation
with a nonlinear Robin boundary condition to mean curvature flow with contact
angle close to 90°. SIAM Journal on Mathematical Analysis. Society for
Industrial and Applied Mathematics. https://doi.org/10.1137/21m1424925
chicago: Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation
with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact
Angle Close to 90°.” SIAM Journal on Mathematical Analysis. Society for
Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21m1424925.
ieee: H. Abels and M. Moser, “Convergence of the Allen--Cahn equation with a nonlinear
Robin boundary condition to mean curvature flow with contact angle close to 90°,”
SIAM Journal on Mathematical Analysis, vol. 54, no. 1. Society for Industrial
and Applied Mathematics, pp. 114–172, 2022.
ista: Abels H, Moser M. 2022. Convergence of the Allen--Cahn equation with a nonlinear
Robin boundary condition to mean curvature flow with contact angle close to 90°.
SIAM Journal on Mathematical Analysis. 54(1), 114–172.
mla: Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation
with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact
Angle Close to 90°.” SIAM Journal on Mathematical Analysis, vol. 54, no.
1, Society for Industrial and Applied Mathematics, 2022, pp. 114–72, doi:10.1137/21m1424925.
short: H. Abels, M. Moser, SIAM Journal on Mathematical Analysis 54 (2022) 114–172.
corr_author: '1'
date_created: 2023-01-16T10:07:00Z
date_published: 2022-01-04T00:00:00Z
date_updated: 2024-10-09T21:03:58Z
day: '04'
department:
- _id: JuFi
doi: 10.1137/21m1424925
external_id:
arxiv:
- '2105.08434'
isi:
- '000762768000004'
intvolume: ' 54'
isi: 1
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2105.08434'
month: '01'
oa: 1
oa_version: Preprint
page: 114-172
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- 1095-7154
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition
to mean curvature flow with contact angle close to 90°
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 54
year: '2022'
...
---
_id: '9039'
abstract:
- lang: eng
text: We give a short and self-contained proof for rates of convergence of the Allen--Cahn
equation towards mean curvature flow, assuming that a classical (smooth) solution
to the latter exists and starting from well-prepared initial data. Our approach
is based on a relative entropy technique. In particular, it does not require a
stability analysis for the linearized Allen--Cahn operator. As our analysis also
does not rely on the comparison principle, we expect it to be applicable to more
complex equations and systems.
acknowledgement: "This work was supported by the European Union's Horizon 2020 Research
and Innovation\r\nProgramme under Marie Sklodowska-Curie grant agreement 665385
and by the Deutsche\r\nForschungsgemeinschaft (DFG, German Research Foundation)
under Germany's Excellence Strategy, EXC-2047/1--390685813."
article_processing_charge: No
article_type: original
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Tim
full_name: Laux, Tim
last_name: Laux
- first_name: Theresa M.
full_name: Simon, Theresa M.
last_name: Simon
citation:
ama: 'Fischer JL, Laux T, Simon TM. Convergence rates of the Allen-Cahn equation
to mean curvature flow: A short proof based on relative entropies. SIAM Journal
on Mathematical Analysis. 2020;52(6):6222-6233. doi:10.1137/20M1322182'
apa: 'Fischer, J. L., Laux, T., & Simon, T. M. (2020). Convergence rates of
the Allen-Cahn equation to mean curvature flow: A short proof based on relative
entropies. SIAM Journal on Mathematical Analysis. Society for Industrial
and Applied Mathematics. https://doi.org/10.1137/20M1322182'
chicago: 'Fischer, Julian L, Tim Laux, and Theresa M. Simon. “Convergence Rates
of the Allen-Cahn Equation to Mean Curvature Flow: A Short Proof Based on Relative
Entropies.” SIAM Journal on Mathematical Analysis. Society for Industrial
and Applied Mathematics, 2020. https://doi.org/10.1137/20M1322182.'
ieee: 'J. L. Fischer, T. Laux, and T. M. Simon, “Convergence rates of the Allen-Cahn
equation to mean curvature flow: A short proof based on relative entropies,” SIAM
Journal on Mathematical Analysis, vol. 52, no. 6. Society for Industrial and
Applied Mathematics, pp. 6222–6233, 2020.'
ista: 'Fischer JL, Laux T, Simon TM. 2020. Convergence rates of the Allen-Cahn equation
to mean curvature flow: A short proof based on relative entropies. SIAM Journal
on Mathematical Analysis. 52(6), 6222–6233.'
mla: 'Fischer, Julian L., et al. “Convergence Rates of the Allen-Cahn Equation to
Mean Curvature Flow: A Short Proof Based on Relative Entropies.” SIAM Journal
on Mathematical Analysis, vol. 52, no. 6, Society for Industrial and Applied
Mathematics, 2020, pp. 6222–33, doi:10.1137/20M1322182.'
short: J.L. Fischer, T. Laux, T.M. Simon, SIAM Journal on Mathematical Analysis
52 (2020) 6222–6233.
corr_author: '1'
date_created: 2021-01-24T23:01:09Z
date_published: 2020-12-15T00:00:00Z
date_updated: 2025-07-10T12:01:32Z
day: '15'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1137/20M1322182
ec_funded: 1
external_id:
isi:
- '000600695200027'
file:
- access_level: open_access
checksum: 21aa1cf4c30a86a00cae15a984819b5d
content_type: application/pdf
creator: dernst
date_created: 2021-01-25T07:48:39Z
date_updated: 2021-01-25T07:48:39Z
file_id: '9041'
file_name: 2020_SIAM_Fischer.pdf
file_size: 310655
relation: main_file
success: 1
file_date_updated: 2021-01-25T07:48:39Z
has_accepted_license: '1'
intvolume: ' 52'
isi: 1
issue: '6'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 6222-6233
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- 1095-7154
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Convergence rates of the Allen-Cahn equation to mean curvature flow: A short
proof based on relative entropies'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 52
year: '2020'
...
---
_id: '71'
abstract:
- lang: eng
text: "We consider dynamical transport metrics for probability measures on discretisations
of a bounded convex domain in ℝd. These metrics are natural discrete counterparts
to the Kantorovich metric \U0001D54E2, defined using a Benamou-Brenier type formula.
Under mild assumptions we prove an asymptotic upper bound for the discrete transport
metric Wt in terms of \U0001D54E2, as the size of the mesh T tends to 0. However,
we show that the corresponding lower bound may fail in general, even on certain
one-dimensional and symmetric two-dimensional meshes. In addition, we show that
the asymptotic lower bound holds under an isotropy assumption on the mesh, which
turns out to be essentially necessary. This assumption is satisfied, e.g., for
tilings by convex regular polygons, and it implies Gromov-Hausdorff convergence
of the transport metric."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Peter
full_name: Gladbach, Peter
last_name: Gladbach
- first_name: Eva
full_name: Kopfer, Eva
last_name: Kopfer
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
citation:
ama: Gladbach P, Kopfer E, Maas J. Scaling limits of discrete optimal transport.
SIAM Journal on Mathematical Analysis. 2020;52(3):2759-2802. doi:10.1137/19M1243440
apa: Gladbach, P., Kopfer, E., & Maas, J. (2020). Scaling limits of discrete
optimal transport. SIAM Journal on Mathematical Analysis. Society for Industrial
and Applied Mathematics. https://doi.org/10.1137/19M1243440
chicago: Gladbach, Peter, Eva Kopfer, and Jan Maas. “Scaling Limits of Discrete
Optimal Transport.” SIAM Journal on Mathematical Analysis. Society for
Industrial and Applied Mathematics, 2020. https://doi.org/10.1137/19M1243440.
ieee: P. Gladbach, E. Kopfer, and J. Maas, “Scaling limits of discrete optimal transport,”
SIAM Journal on Mathematical Analysis, vol. 52, no. 3. Society for Industrial
and Applied Mathematics, pp. 2759–2802, 2020.
ista: Gladbach P, Kopfer E, Maas J. 2020. Scaling limits of discrete optimal transport.
SIAM Journal on Mathematical Analysis. 52(3), 2759–2802.
mla: Gladbach, Peter, et al. “Scaling Limits of Discrete Optimal Transport.” SIAM
Journal on Mathematical Analysis, vol. 52, no. 3, Society for Industrial and
Applied Mathematics, 2020, pp. 2759–802, doi:10.1137/19M1243440.
short: P. Gladbach, E. Kopfer, J. Maas, SIAM Journal on Mathematical Analysis 52
(2020) 2759–2802.
date_created: 2018-12-11T11:44:28Z
date_published: 2020-10-01T00:00:00Z
date_updated: 2025-07-10T11:54:14Z
day: '01'
department:
- _id: JaMa
doi: 10.1137/19M1243440
external_id:
arxiv:
- '1809.01092'
isi:
- '000546975100017'
intvolume: ' 52'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1809.01092
month: '10'
oa: 1
oa_version: Preprint
page: 2759-2802
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- 1095-7154
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
publist_id: '7983'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scaling limits of discrete optimal transport
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 52
year: '2020'
...
---
_id: '9781'
abstract:
- lang: eng
text: We consider the Pekar functional on a ball in ℝ3. We prove uniqueness of minimizers,
and a quadratic lower bound in terms of the distance to the minimizer. The latter
follows from nondegeneracy of the Hessian at the minimum.
acknowledgement: We are grateful for the hospitality at the Mittag-Leffler Institute,
where part of this work has been done. The work of the authors was supported by
the European Research Council (ERC)under the European Union's Horizon 2020 research
and innovation programme grant 694227.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Dario
full_name: Feliciangeli, Dario
id: 41A639AA-F248-11E8-B48F-1D18A9856A87
last_name: Feliciangeli
orcid: 0000-0003-0754-8530
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Feliciangeli D, Seiringer R. Uniqueness and nondegeneracy of minimizers of
the Pekar functional on a ball. SIAM Journal on Mathematical Analysis.
2020;52(1):605-622. doi:10.1137/19m126284x
apa: Feliciangeli, D., & Seiringer, R. (2020). Uniqueness and nondegeneracy
of minimizers of the Pekar functional on a ball. SIAM Journal on Mathematical
Analysis. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/19m126284x
chicago: Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy
of Minimizers of the Pekar Functional on a Ball.” SIAM Journal on Mathematical
Analysis. Society for Industrial and Applied Mathematics , 2020. https://doi.org/10.1137/19m126284x.
ieee: D. Feliciangeli and R. Seiringer, “Uniqueness and nondegeneracy of minimizers
of the Pekar functional on a ball,” SIAM Journal on Mathematical Analysis,
vol. 52, no. 1. Society for Industrial and Applied Mathematics , pp. 605–622,
2020.
ista: Feliciangeli D, Seiringer R. 2020. Uniqueness and nondegeneracy of minimizers
of the Pekar functional on a ball. SIAM Journal on Mathematical Analysis. 52(1),
605–622.
mla: Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of
Minimizers of the Pekar Functional on a Ball.” SIAM Journal on Mathematical
Analysis, vol. 52, no. 1, Society for Industrial and Applied Mathematics ,
2020, pp. 605–22, doi:10.1137/19m126284x.
short: D. Feliciangeli, R. Seiringer, SIAM Journal on Mathematical Analysis 52 (2020)
605–622.
corr_author: '1'
date_created: 2021-08-06T07:34:16Z
date_published: 2020-02-12T00:00:00Z
date_updated: 2026-04-08T06:59:49Z
day: '12'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1137/19m126284x
ec_funded: 1
external_id:
arxiv:
- '1904.08647 '
isi:
- '000546967700022'
has_accepted_license: '1'
intvolume: ' 52'
isi: 1
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1904.08647
month: '02'
oa: 1
oa_version: Preprint
page: 605-622
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- 1095-7154
issn:
- 0036-1410
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
quality_controlled: '1'
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relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball
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short: CC BY-NC-ND (4.0)
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volume: 52
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...