English

Non-local approximation of free-discontinuity problems in linear elasticity and application to stochastic homogenisation

Analysis of PDEs 2024-11-20 v1 Functional Analysis

Abstract

We analyse the Γ\Gamma-convergence of general non-local convolution type functionals with varying densities depending on the space variable and on the symmetrized gradient. The limit is a local free-discontinuity functional, where the bulk term can be completely characterized in terms of an asymptotic cell formula. From that, we can deduce an homogenisation result in the stochastic setting.

Keywords

Cite

@article{arxiv.2212.13759,
  title  = {Non-local approximation of free-discontinuity problems in linear elasticity and application to stochastic homogenisation},
  author = {Roberta Marziani and Francesco Solombrino},
  journal= {arXiv preprint arXiv:2212.13759},
  year   = {2024}
}