Mission $p<n-1$: Possible -- Nonlinear Elasticity Beyond Conventional Limits
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908408468209664 |
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| 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 |