English

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 p<n1p<n-1. Our class of admissible deformations consists of weak limits of Sobolev W1,pW^{1,p} 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.

Keywords

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)

R2 v1 2026-07-01T03:06:38.594Z