A global method for deterministic and stochastic homogenisation in BV

In this paper we study the deterministic and stochastic homogenisation of free-discontinuity functionals under linear growth and coercivity conditions. The main novelty of our deterministic result is that we work under very general assumptions on the integrands which, in particular, are not required...

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Autores principales: Cagnetti, Filippo, Dal Maso, Gianni, Scardia, Lucia, Zeppieri, Caterina Ida
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2022
Materias:
Manuscript
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8989869/
https://www.ncbi.nlm.nih.gov/pubmed/35465087
http://dx.doi.org/10.1007/s40818-022-00119-4
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author Cagnetti, Filippo
Dal Maso, Gianni
Scardia, Lucia
Zeppieri, Caterina Ida
author_facet Cagnetti, Filippo
Dal Maso, Gianni
Scardia, Lucia
Zeppieri, Caterina Ida
author_sort Cagnetti, Filippo
collection PubMed
description In this paper we study the deterministic and stochastic homogenisation of free-discontinuity functionals under linear growth and coercivity conditions. The main novelty of our deterministic result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Combining this result with the pointwise Subadditive Ergodic Theorem by Akcoglu and Krengel, we prove a stochastic homogenisation result, in the case of stationary random integrands. In particular, we characterise the limit integrands in terms of asymptotic cell formulas, as in the classical case of periodic homogenisation.
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spelling pubmed-89898692022-04-22 A global method for deterministic and stochastic homogenisation in BV Cagnetti, Filippo Dal Maso, Gianni Scardia, Lucia Zeppieri, Caterina Ida Ann PDE Manuscript In this paper we study the deterministic and stochastic homogenisation of free-discontinuity functionals under linear growth and coercivity conditions. The main novelty of our deterministic result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Combining this result with the pointwise Subadditive Ergodic Theorem by Akcoglu and Krengel, we prove a stochastic homogenisation result, in the case of stationary random integrands. In particular, we characterise the limit integrands in terms of asymptotic cell formulas, as in the classical case of periodic homogenisation. Springer International Publishing 2022-04-07 2022 /pmc/articles/PMC8989869/ /pubmed/35465087 http://dx.doi.org/10.1007/s40818-022-00119-4 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Manuscript
Cagnetti, Filippo
Dal Maso, Gianni
Scardia, Lucia
Zeppieri, Caterina Ida
A global method for deterministic and stochastic homogenisation in BV
title A global method for deterministic and stochastic homogenisation in BV
title_full A global method for deterministic and stochastic homogenisation in BV
title_fullStr A global method for deterministic and stochastic homogenisation in BV
title_full_unstemmed A global method for deterministic and stochastic homogenisation in BV
title_short A global method for deterministic and stochastic homogenisation in BV
title_sort global method for deterministic and stochastic homogenisation in bv
topic Manuscript
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8989869/
https://www.ncbi.nlm.nih.gov/pubmed/35465087
http://dx.doi.org/10.1007/s40818-022-00119-4
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