Mission $p<n-1$: Possible -- Nonlinear Elasticity Beyond Conventional Limits
Analysis of PDEs
2025-06-17 v2
Abstract
In this paper we prove the lower semicontinuity of a Neohookean-type energy for a model of Nonlinear Elasticity that allows, for the first time, for . Our class of admissible deformations consists of weak limits of Sobolev homeomorphisms. We also introduce a model that allows for cavitations by studying weak limits of homeomorphisms that can open cavities at some points. In this model we add the measure of the created surface to the energy functional and for this functional we again prove lower semicontinuity.
Cite
@article{arxiv.2506.07543,
title = {Mission $p<n-1$: Possible -- Nonlinear Elasticity Beyond Conventional Limits},
author = {Daniel Campbell and Anna Doležalová and Stanislav Hencl},
journal= {arXiv preprint arXiv:2506.07543},
year = {2025}
}
Comments
Corrected typos, most importantly in equation (1.1)