---
OA_place: publisher
OA_type: hybrid
_id: '13129'
abstract:
- lang: eng
text: "We study the representative volume element (RVE) method, which is a method
to approximately infer the effective behavior ahom of a stationary random medium.
The latter is described by a coefficient field a(x) generated from a given ensemble
⟨⋅⟩ and the corresponding linear elliptic operator −∇⋅a∇. In line with the theory
of homogenization, the method proceeds by computing d=3 correctors (d denoting
the space dimension). To be numerically tractable, this computation has to be
done on a finite domain: the so-called representative volume element, i.e., a
large box with, say, periodic boundary conditions. The main message of this article
is: Periodize the ensemble instead of its realizations. By this, we mean that
it is better to sample from a suitably periodized ensemble than to periodically
extend the restriction of a realization a(x) from the whole-space ensemble ⟨⋅⟩.
We make this point by investigating the bias (or systematic error), i.e., the
difference between ahom and the expected value of the RVE method, in terms of
its scaling w.r.t. the lateral size L of the box. In case of periodizing a(x),
we heuristically argue that this error is generically O(L−1). In case of a suitable
periodization of ⟨⋅⟩\r\n, we rigorously show that it is O(L−d). In fact, we give
a characterization of the leading-order error term for both strategies and argue
that even in the isotropic case it is generically non-degenerate. We carry out
the rigorous analysis in the convenient setting of ensembles ⟨⋅⟩\r\n of Gaussian
type, which allow for a straightforward periodization, passing via the (integrable)
covariance function. This setting has also the advantage of making the Price theorem
and the Malliavin calculus available for optimal stochastic estimates of correctors.
We actually need control of second-order correctors to capture the leading-order
error term. This is due to inversion symmetry when applying the two-scale expansion
to the Green function. As a bonus, we present a stream-lined strategy to estimate
the error in a higher-order two-scale expansion of the Green function."
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Nicolas
full_name: Clozeau, Nicolas
id: fea1b376-906f-11eb-847d-b2c0cf46455b
last_name: Clozeau
- first_name: Marc
full_name: Josien, Marc
last_name: Josien
- first_name: Felix
full_name: Otto, Felix
last_name: Otto
- first_name: Qiang
full_name: Xu, Qiang
last_name: Xu
citation:
ama: 'Clozeau N, Josien M, Otto F, Xu Q. Bias in the representative volume element
method: Periodize the ensemble instead of its realizations. Foundations of
Computational Mathematics. 2024;24:1305-1387. doi:10.1007/s10208-023-09613-y'
apa: 'Clozeau, N., Josien, M., Otto, F., & Xu, Q. (2024). Bias in the representative
volume element method: Periodize the ensemble instead of its realizations. Foundations
of Computational Mathematics. Springer Nature. https://doi.org/10.1007/s10208-023-09613-y'
chicago: 'Clozeau, Nicolas, Marc Josien, Felix Otto, and Qiang Xu. “Bias in the
Representative Volume Element Method: Periodize the Ensemble Instead of Its Realizations.”
Foundations of Computational Mathematics. Springer Nature, 2024. https://doi.org/10.1007/s10208-023-09613-y.'
ieee: 'N. Clozeau, M. Josien, F. Otto, and Q. Xu, “Bias in the representative volume
element method: Periodize the ensemble instead of its realizations,” Foundations
of Computational Mathematics, vol. 24. Springer Nature, pp. 1305–1387, 2024.'
ista: 'Clozeau N, Josien M, Otto F, Xu Q. 2024. Bias in the representative volume
element method: Periodize the ensemble instead of its realizations. Foundations
of Computational Mathematics. 24, 1305–1387.'
mla: 'Clozeau, Nicolas, et al. “Bias in the Representative Volume Element Method:
Periodize the Ensemble Instead of Its Realizations.” Foundations of Computational
Mathematics, vol. 24, Springer Nature, 2024, pp. 1305–87, doi:10.1007/s10208-023-09613-y.'
short: N. Clozeau, M. Josien, F. Otto, Q. Xu, Foundations of Computational Mathematics
24 (2024) 1305–1387.
corr_author: '1'
date_created: 2023-06-11T22:00:40Z
date_published: 2024-08-01T00:00:00Z
date_updated: 2025-01-09T07:37:50Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s10208-023-09613-y
external_id:
isi:
- '000999623100001'
file:
- access_level: open_access
checksum: ec0582e2b55e2703a7da2686ae0d682e
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T07:36:57Z
date_updated: 2025-01-09T07:36:57Z
file_id: '18782'
file_name: 2024_FoundCompMath_Clozeau.pdf
file_size: 1454406
relation: main_file
success: 1
file_date_updated: 2025-01-09T07:36:57Z
has_accepted_license: '1'
intvolume: ' 24'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '08'
oa: 1
oa_version: Published Version
page: 1305-1387
publication: Foundations of Computational Mathematics
publication_identifier:
eissn:
- 1615-3383
issn:
- 1615-3375
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Bias in the representative volume element method: Periodize the ensemble instead
of its realizations'
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: 24
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '14797'
abstract:
- lang: eng
text: We study a random matching problem on closed compact 2 -dimensional Riemannian
manifolds (with respect to the squared Riemannian distance), with samples of random
points whose common law is absolutely continuous with respect to the volume measure
with strictly positive and bounded density. We show that given two sequences of
numbers n and m=m(n) of points, asymptotically equivalent as n goes to infinity,
the optimal transport plan between the two empirical measures μn and νm is
quantitatively well-approximated by (Id,exp(∇hn))#μn where hn solves a linear
elliptic PDE obtained by a regularized first-order linearization of the Monge-Ampère
equation. This is obtained in the case of samples of correlated random points
for which a stretched exponential decay of the α -mixing coefficient holds and
for a class of discrete-time Markov chains having a unique absolutely continuous
invariant measure with respect to the volume measure.
acknowledgement: "NC has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme (Grant
agreement No 948819).\r\nFM is supported by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) through the SPP 2265 Random Geometric Systems.
FM has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) under Germany’s Excellence Strategy EXC 2044 -390685587, Mathematics
Münster: Dynamics–Geometry–Structure. FM has been funded by the Max Planck Institute
for Mathematics in the Sciences."
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Nicolas
full_name: Clozeau, Nicolas
id: fea1b376-906f-11eb-847d-b2c0cf46455b
last_name: Clozeau
- first_name: Francesco
full_name: Mattesini, Francesco
last_name: Mattesini
citation:
ama: Clozeau N, Mattesini F. Annealed quantitative estimates for the quadratic 2D-discrete
random matching problem. Probability Theory and Related Fields. 2024;190:485-541.
doi:10.1007/s00440-023-01254-0
apa: Clozeau, N., & Mattesini, F. (2024). Annealed quantitative estimates for
the quadratic 2D-discrete random matching problem. Probability Theory and Related
Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01254-0
chicago: Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates
for the Quadratic 2D-Discrete Random Matching Problem.” Probability Theory
and Related Fields. Springer Nature, 2024. https://doi.org/10.1007/s00440-023-01254-0.
ieee: N. Clozeau and F. Mattesini, “Annealed quantitative estimates for the quadratic
2D-discrete random matching problem,” Probability Theory and Related Fields,
vol. 190. Springer Nature, pp. 485–541, 2024.
ista: Clozeau N, Mattesini F. 2024. Annealed quantitative estimates for the quadratic
2D-discrete random matching problem. Probability Theory and Related Fields. 190,
485–541.
mla: Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates
for the Quadratic 2D-Discrete Random Matching Problem.” Probability Theory
and Related Fields, vol. 190, Springer Nature, 2024, pp. 485–541, doi:10.1007/s00440-023-01254-0.
short: N. Clozeau, F. Mattesini, Probability Theory and Related Fields 190 (2024)
485–541.
corr_author: '1'
date_created: 2024-01-14T23:00:57Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2025-09-04T11:43:43Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00440-023-01254-0
ec_funded: 1
external_id:
arxiv:
- '2303.00353'
isi:
- '001136206200002'
file:
- access_level: open_access
checksum: 34f44cad6a210ff66791ee37e590af2c
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T08:10:54Z
date_updated: 2025-01-09T08:10:54Z
file_id: '18788'
file_name: 2024_ProbTheoryRelatFields_Clozeau.pdf
file_size: 880117
relation: main_file
success: 1
file_date_updated: 2025-01-09T08:10:54Z
has_accepted_license: '1'
intvolume: ' 190'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 485-541
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Annealed quantitative estimates for the quadratic 2D-discrete random matching
problem
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 190
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '17462'
abstract:
- lang: eng
text: We are interested in numerical algorithms for computing the electrical field
generated by a charge distribution localized on scale l in an infinite heterogeneous
correlated random medium, in a situation where the medium is only known in a box
of diameter L >>l around the support of the charge. We show that the algorithm
in [J. Lu, F. Otto, and L. Wang, Optimal Artificial Boundary Conditions Based
on Second-Order Correctors for Three Dimensional Random Ellilptic Media, preprint,
arXiv:2109.01616, 2021], suggesting optimal Dirichlet boundary conditions motivated
by the multipole expansion [P. Bella, A. Giunti, and F. Otto, Comm. Partial Differential
Equations, 45 (2020), pp. 561–640], still performs well in correlated media. With
overwhelming probability, we obtain a convergence rate in terms of l, L, and the
size of the correlations for which optimality is supported with numerical simulations.
These estimates are provided for ensembles which satisfy a multiscale logarithmic
Sobolev inequality, where our main tool is an extension of the semigroup estimates
in [N. Clozeau, Stoch. Partial Differ. Equ. Anal. Comput., 11 (2023), pp. 1254–1378].
As part of our strategy, we construct sublinear second-order correctors in this
correlated setting, which is of independent interest.
acknowledgement: We would like to thank our affiliations, Institute of Science and
Technology Austria and Max Planck Institute for Mathematics in the Sciences, for
supporting the authors’ visits to each other, which greatly facilitated this work.
We would like to thank Marc Josien and Quinn Winters for assistance in numerical
implementation.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nicolas
full_name: Clozeau, Nicolas
id: fea1b376-906f-11eb-847d-b2c0cf46455b
last_name: Clozeau
- first_name: Lihan
full_name: Wang, Lihan
last_name: Wang
citation:
ama: Clozeau N, Wang L. Artificial boundary conditions for random elliptic systems
with correlated coefficient field. Multiscale Modeling and Simulation.
2024;22(3):973-1029. doi:10.1137/23M1603819
apa: Clozeau, N., & Wang, L. (2024). Artificial boundary conditions for random
elliptic systems with correlated coefficient field. Multiscale Modeling and
Simulation. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/23M1603819
chicago: Clozeau, Nicolas, and Lihan Wang. “Artificial Boundary Conditions for Random
Elliptic Systems with Correlated Coefficient Field.” Multiscale Modeling and
Simulation. Society for Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/23M1603819.
ieee: N. Clozeau and L. Wang, “Artificial boundary conditions for random elliptic
systems with correlated coefficient field,” Multiscale Modeling and Simulation,
vol. 22, no. 3. Society for Industrial and Applied Mathematics, pp. 973–1029,
2024.
ista: Clozeau N, Wang L. 2024. Artificial boundary conditions for random elliptic
systems with correlated coefficient field. Multiscale Modeling and Simulation.
22(3), 973–1029.
mla: Clozeau, Nicolas, and Lihan Wang. “Artificial Boundary Conditions for Random
Elliptic Systems with Correlated Coefficient Field.” Multiscale Modeling and
Simulation, vol. 22, no. 3, Society for Industrial and Applied Mathematics,
2024, pp. 973–1029, doi:10.1137/23M1603819.
short: N. Clozeau, L. Wang, Multiscale Modeling and Simulation 22 (2024) 973–1029.
corr_author: '1'
date_created: 2024-08-25T22:01:08Z
date_published: 2024-09-01T00:00:00Z
date_updated: 2025-09-08T09:01:00Z
day: '01'
department:
- _id: JuFi
doi: 10.1137/23M1603819
ec_funded: 1
external_id:
arxiv:
- '2309.06798'
isi:
- '001285416500001'
intvolume: ' 22'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2309.06798
month: '09'
oa: 1
oa_version: Preprint
page: 973-1029
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Multiscale Modeling and Simulation
publication_identifier:
eissn:
- 1540-3467
issn:
- 1540-3459
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Artificial boundary conditions for random elliptic systems with correlated
coefficient field
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 22
year: '2024'
...
---
_id: '10173'
abstract:
- lang: eng
text: We study the large scale behavior of elliptic systems with stationary random
coefficient that have only slowly decaying correlations. To this aim we analyze
the so-called corrector equation, a degenerate elliptic equation posed in the
probability space. In this contribution, we use a parabolic approach and optimally
quantify the time decay of the semigroup. For the theoretical point of view, we
prove an optimal decay estimate of the gradient and flux of the corrector when
spatially averaged over a scale R larger than 1. For the numerical point of view,
our results provide convenient tools for the analysis of various numerical methods.
acknowledgement: "I would like to thank my advisor Antoine Gloria for suggesting this
problem to me, as well for many interesting discussions and suggestions.\r\nOpen
access funding provided by Institute of Science and Technology (IST Austria)."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Nicolas
full_name: Clozeau, Nicolas
id: fea1b376-906f-11eb-847d-b2c0cf46455b
last_name: Clozeau
citation:
ama: 'Clozeau N. Optimal decay of the parabolic semigroup in stochastic homogenization
for correlated coefficient fields. Stochastics and Partial Differential Equations:
Analysis and Computations. 2023;11:1254–1378. doi:10.1007/s40072-022-00254-w'
apa: 'Clozeau, N. (2023). Optimal decay of the parabolic semigroup in stochastic
homogenization for correlated coefficient fields. Stochastics and Partial
Differential Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-022-00254-w'
chicago: 'Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic
Homogenization for Correlated Coefficient Fields.” Stochastics and Partial
Differential Equations: Analysis and Computations. Springer Nature, 2023.
https://doi.org/10.1007/s40072-022-00254-w.'
ieee: 'N. Clozeau, “Optimal decay of the parabolic semigroup in stochastic homogenization
for correlated coefficient fields,” Stochastics and Partial Differential Equations:
Analysis and Computations, vol. 11. Springer Nature, pp. 1254–1378, 2023.'
ista: 'Clozeau N. 2023. Optimal decay of the parabolic semigroup in stochastic homogenization
for correlated coefficient fields. Stochastics and Partial Differential Equations:
Analysis and Computations. 11, 1254–1378.'
mla: 'Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic
Homogenization for Correlated Coefficient Fields.” Stochastics and Partial
Differential Equations: Analysis and Computations, vol. 11, Springer Nature,
2023, pp. 1254–1378, doi:10.1007/s40072-022-00254-w.'
short: 'N. Clozeau, Stochastics and Partial Differential Equations: Analysis and
Computations 11 (2023) 1254–1378.'
corr_author: '1'
date_created: 2021-10-23T10:50:22Z
date_published: 2023-09-01T00:00:00Z
date_updated: 2024-10-09T21:01:04Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s40072-022-00254-w
external_id:
arxiv:
- '2102.07452'
isi:
- '000799715600001'
file:
- access_level: open_access
checksum: f83dcaecdbd3ace862c4ed97a20e8501
content_type: application/pdf
creator: dernst
date_created: 2023-08-14T11:51:04Z
date_updated: 2023-08-14T11:51:04Z
file_id: '14052'
file_name: 2023_StochPartialDiffEquations_Clozeau.pdf
file_size: 1635193
relation: main_file
success: 1
file_date_updated: 2023-08-14T11:51:04Z
has_accepted_license: '1'
intvolume: ' 11'
isi: 1
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 1254–1378
publication: 'Stochastics and Partial Differential Equations: Analysis and Computations'
publication_identifier:
issn:
- 2194-0401
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal decay of the parabolic semigroup in stochastic homogenization for
correlated coefficient fields
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: 11
year: '2023'
...
---
OA_type: green
_id: '10174'
abstract:
- lang: eng
text: Quantitative stochastic homogenization of linear elliptic operators is by
now well-understood. In this contribution we move forward to the nonlinear setting
of monotone operators with p-growth. This first work is dedicated to a quantitative
two-scale expansion result. Fluctuations will be addressed in companion articles.
By treating the range of exponents 2≤p<∞ in dimensions d≤3, we are able to consider
genuinely nonlinear elliptic equations and systems such as −∇⋅A(x)(1+|∇u|p−2)∇u=f
(with A random, non-necessarily symmetric) for the first time. When going from
p=2 to p>2, the main difficulty is to analyze the associated linearized operator,
whose coefficients are degenerate, unbounded, and depend on the random input A
via the solution of a nonlinear equation. One of our main achievements is the
control of this intricate nonlinear dependence, leading to annealed Meyers' estimates
for the linearized operator, which are key to the quantitative two-scale expansion
result.
acknowledgement: The authors warmly thank Mitia Duerinckx for discussions on annealed
estimates, and Mathias Schäffner for pointing out that the conditions of [14] apply
to ̄a in the setting of Theorem 2.2 and for discussions on regularity theory for
operators with non-standard growth conditions. The authors received financial support
from the European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (Grant Agreement n◦ 864066).
article_number: '67'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nicolas
full_name: Clozeau, Nicolas
id: fea1b376-906f-11eb-847d-b2c0cf46455b
last_name: Clozeau
- first_name: Antoine
full_name: Gloria, Antoine
last_name: Gloria
citation:
ama: 'Clozeau N, Gloria A. Quantitative nonlinear homogenization: Control of oscillations.
Archive for Rational Mechanics and Analysis . 247(4). doi:10.1007/s00205-023-01895-4'
apa: 'Clozeau, N., & Gloria, A. (n.d.). Quantitative nonlinear homogenization:
Control of oscillations. Archive for Rational Mechanics and Analysis .
Springer Nature. https://doi.org/10.1007/s00205-023-01895-4'
chicago: 'Clozeau, Nicolas, and Antoine Gloria. “Quantitative Nonlinear Homogenization:
Control of Oscillations.” Archive for Rational Mechanics and Analysis .
Springer Nature, n.d. https://doi.org/10.1007/s00205-023-01895-4.'
ieee: 'N. Clozeau and A. Gloria, “Quantitative nonlinear homogenization: Control
of oscillations,” Archive for Rational Mechanics and Analysis , vol. 247,
no. 4. Springer Nature.'
ista: 'Clozeau N, Gloria A. Quantitative nonlinear homogenization: Control of oscillations.
Archive for Rational Mechanics and Analysis . 247(4), 67.'
mla: 'Clozeau, Nicolas, and Antoine Gloria. “Quantitative Nonlinear Homogenization:
Control of Oscillations.” Archive for Rational Mechanics and Analysis ,
vol. 247, no. 4, 67, Springer Nature, doi:10.1007/s00205-023-01895-4.'
short: N. Clozeau, A. Gloria, Archive for Rational Mechanics and Analysis 247 (n.d.).
date_created: 2021-10-23T10:50:55Z
date_published: 2023-07-16T00:00:00Z
date_updated: 2025-01-20T14:44:10Z
day: '16'
doi: 10.1007/s00205-023-01895-4
extern: '1'
external_id:
arxiv:
- '2104.04263'
intvolume: ' 247'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2104.04263
month: '07'
oa: 1
oa_version: Preprint
publication: 'Archive for Rational Mechanics and Analysis '
publication_identifier:
eissn:
- 1432-0673
issn:
- 0003-9527
publication_status: draft
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Quantitative nonlinear homogenization: Control of oscillations'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 247
year: '2023'
...
---
_id: '10175'
abstract:
- lang: eng
text: We study periodic homogenization by Γ-convergence of integral functionals
with integrands W(x,ξ) having no polynomial growth and which are both not necessarily
continuous with respect to the space variable and not necessarily convex with
respect to the matrix variable. This allows to deal with homogenization of composite
hyperelastic materials consisting of two or more periodic components whose the
energy densities tend to infinity as the volume of matter tends to zero, i.e.,
W(x,ξ)=∑j∈J1Vj(x)Hj(ξ) where {Vj}j∈J is a finite family of open disjoint subsets
of RN, with |∂Vj|=0 for all j∈J and ∣∣RN∖⋃j∈JVj|=0, and, for each j∈J, Hj(ξ)→∞
as detξ→0. In fact, our results apply to integrands of type W(x,ξ)=a(x)H(ξ) when
H(ξ)→∞ as detξ→0 and a∈L∞(RN;[0,∞[) is 1-periodic and is either continuous almost
everywhere or not continuous. When a is not continuous, we obtain a density homogenization
formula which is a priori different from the classical one by Braides–Müller.
Although applications to hyperelasticity are limited due to the fact that our
framework is not consistent with the constraint of noninterpenetration of the
matter, our results can be of technical interest to analysis of homogenization
of integral functionals.
article_processing_charge: No
article_type: original
author:
- first_name: Omar
full_name: Anza Hafsa, Omar
last_name: Anza Hafsa
- first_name: Nicolas
full_name: Clozeau, Nicolas
id: fea1b376-906f-11eb-847d-b2c0cf46455b
last_name: Clozeau
- first_name: Jean-Philippe
full_name: Mandallena, Jean-Philippe
last_name: Mandallena
citation:
ama: Anza Hafsa O, Clozeau N, Mandallena J-P. Homogenization of nonconvex unbounded
singular integrals. Annales mathématiques Blaise Pascal. 2017;24(2):135-193.
doi:10.5802/ambp.367
apa: Anza Hafsa, O., Clozeau, N., & Mandallena, J.-P. (2017). Homogenization
of nonconvex unbounded singular integrals. Annales Mathématiques Blaise Pascal.
Université Clermont Auvergne. https://doi.org/10.5802/ambp.367
chicago: Anza Hafsa, Omar, Nicolas Clozeau, and Jean-Philippe Mandallena. “Homogenization
of Nonconvex Unbounded Singular Integrals.” Annales Mathématiques Blaise Pascal.
Université Clermont Auvergne, 2017. https://doi.org/10.5802/ambp.367.
ieee: O. Anza Hafsa, N. Clozeau, and J.-P. Mandallena, “Homogenization of nonconvex
unbounded singular integrals,” Annales mathématiques Blaise Pascal, vol.
24, no. 2. Université Clermont Auvergne, pp. 135–193, 2017.
ista: Anza Hafsa O, Clozeau N, Mandallena J-P. 2017. Homogenization of nonconvex
unbounded singular integrals. Annales mathématiques Blaise Pascal. 24(2), 135–193.
mla: Anza Hafsa, Omar, et al. “Homogenization of Nonconvex Unbounded Singular Integrals.”
Annales Mathématiques Blaise Pascal, vol. 24, no. 2, Université Clermont
Auvergne, 2017, pp. 135–93, doi:10.5802/ambp.367.
short: O. Anza Hafsa, N. Clozeau, J.-P. Mandallena, Annales Mathématiques Blaise
Pascal 24 (2017) 135–193.
date_created: 2021-10-23T10:54:23Z
date_published: 2017-11-20T00:00:00Z
date_updated: 2021-10-28T15:16:25Z
day: '20'
ddc:
- '510'
doi: 10.5802/ambp.367
extern: '1'
file:
- access_level: open_access
checksum: 18f40d13dc5d1e24438260b1875b886f
content_type: application/pdf
creator: cziletti
date_created: 2021-10-28T15:02:56Z
date_updated: 2021-10-28T15:02:56Z
file_id: '10194'
file_name: 2017_AMBP_AnzaHafsa.pdf
file_size: 850726
relation: main_file
success: 1
file_date_updated: 2021-10-28T15:02:56Z
has_accepted_license: '1'
intvolume: ' 24'
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nd/3.0/
month: '11'
oa: 1
oa_version: Published Version
page: 135-193
publication: Annales mathématiques Blaise Pascal
publication_identifier:
eissn:
- 2118-7436
issn:
- 1259-1734
publication_status: published
publisher: Université Clermont Auvergne
quality_controlled: '1'
status: public
title: Homogenization of nonconvex unbounded singular integrals
tmp:
image: /images/cc_by_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nd/3.0/legalcode
name: Creative Commons Attribution-NoDerivs 3.0 Unported (CC BY-ND 3.0)
short: CC BY-ND (3.0)
type: journal_article
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 24
year: '2017'
...