---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21881'
abstract:
- lang: eng
  text: "I review recent contributions on nonlinear Dirichlet forms. Then, I specialise
    to the case of 2-\r\nhomogeneous and local forms. Inspired by the theory of Finsler
    manifolds and metric measure spaces, I establish new properties of such nonlinear
    Dirichlet forms, which are reminiscent of differential calculus formulae."
acknowledgement: I am thankful to G. Savaré, for introducing me to the study of nonlinear
  Dirichlet forms and metric measure spaces, and to D. Manini for stimulating discussions.
  Open access funding provided by Institute of Science and Technology (IST Austria).
  The author has been funded by the European Union’s Horizon 2020 research and innovation
  program under the Marie Skłodowska-Curie grant agreement No 754362. Partial support
  has been obtained from the EFI ANR-17-CE40-0030 Project of the French National Research
  Agency.
article_number: '33'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Giovanni
  full_name: Brigati, Giovanni
  id: 63ff57e8-1fbb-11ee-88f2-f558ffc59cf1
  last_name: Brigati
citation:
  ama: Brigati G. Nonlinear Dirichlet forms, energy spaces, and calculus rules. <i>La
    Matematica</i>. 2026;5(2). doi:<a href="https://doi.org/10.1007/s44007-026-00217-w">10.1007/s44007-026-00217-w</a>
  apa: Brigati, G. (2026). Nonlinear Dirichlet forms, energy spaces, and calculus
    rules. <i>La Matematica</i>. Springer Nature. <a href="https://doi.org/10.1007/s44007-026-00217-w">https://doi.org/10.1007/s44007-026-00217-w</a>
  chicago: Brigati, Giovanni. “Nonlinear Dirichlet Forms, Energy Spaces, and Calculus
    Rules.” <i>La Matematica</i>. Springer Nature, 2026. <a href="https://doi.org/10.1007/s44007-026-00217-w">https://doi.org/10.1007/s44007-026-00217-w</a>.
  ieee: G. Brigati, “Nonlinear Dirichlet forms, energy spaces, and calculus rules,”
    <i>La Matematica</i>, vol. 5, no. 2. Springer Nature, 2026.
  ista: Brigati G. 2026. Nonlinear Dirichlet forms, energy spaces, and calculus rules.
    La Matematica. 5(2), 33.
  mla: Brigati, Giovanni. “Nonlinear Dirichlet Forms, Energy Spaces, and Calculus
    Rules.” <i>La Matematica</i>, vol. 5, no. 2, 33, Springer Nature, 2026, doi:<a
    href="https://doi.org/10.1007/s44007-026-00217-w">10.1007/s44007-026-00217-w</a>.
  short: G. Brigati, La Matematica 5 (2026).
corr_author: '1'
date_created: 2026-05-17T22:02:10Z
date_published: 2026-04-29T00:00:00Z
date_updated: 2026-05-18T08:27:08Z
day: '29'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s44007-026-00217-w
external_id:
  arxiv:
  - '2309.00377'
file:
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  creator: dernst
  date_created: 2026-05-18T08:26:15Z
  date_updated: 2026-05-18T08:26:15Z
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has_accepted_license: '1'
intvolume: '         5'
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '04'
oa: 1
oa_version: Published Version
publication: La Matematica
publication_identifier:
  eissn:
  - 2730-9657
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Nonlinear Dirichlet forms, energy spaces, and calculus rules
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: 5
year: '2026'
...