Mission $p<n-1$: Possible -- Nonlinear Elasticity Beyond Conventional Limits

Fuente: arXiv
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Main Authors: Campbell, Daniel, Doležalová, Anna, Hencl, Stanislav
Format: Preprint
Published: 2025
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_version_ 1866908408468209664
author Campbell, Daniel
Doležalová, Anna
Hencl, Stanislav
author_facet Campbell, Daniel
Doležalová, Anna
Hencl, Stanislav
contents 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 $p<n-1$. Our class of admissible deformations consists of weak limits of Sobolev $W^{1,p}$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2506_07543
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Mission $p<n-1$: Possible -- Nonlinear Elasticity Beyond Conventional Limits
Campbell, Daniel
Doležalová, Anna
Hencl, Stanislav
Analysis of PDEs
49J45
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 $p<n-1$. Our class of admissible deformations consists of weak limits of Sobolev $W^{1,p}$ 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.
title Mission $p<n-1$: Possible -- Nonlinear Elasticity Beyond Conventional Limits
topic Analysis of PDEs
49J45
url https://arxiv.org/abs/2506.07543