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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.12885 |
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| _version_ | 1866917774031323136 |
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| author | Dengler, Marcel |
| author_facet | Dengler, Marcel |
| contents | In this work our main objective is to establish various (high frequency-) uniqueness criteria. Initially, we consider $p-$Dirichlet type functionals on a suitable class of measure preserving maps $u: B\subset \mathbb{R}^2 \mapsto \mathbb{R}^2,$ $B$ being the unit disk, and subject to suitable boundary conditions. In the second part we focus on a very similar situations only exchanging the previous functionals by a suitable class of $p-$growing polyconvex functionals and allowing the maps to be arbitrary. In both cases a particular emphasis is laid on high pressure situations, where only uniqueness for a subclass, containing solely of variations with high enough Fourier-modes, can be obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_12885 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | (High frequency)-uniqueness criteria for p-growth functionals in in- and compressible elasticity Dengler, Marcel Analysis of PDEs 74G30, 74B20 In this work our main objective is to establish various (high frequency-) uniqueness criteria. Initially, we consider $p-$Dirichlet type functionals on a suitable class of measure preserving maps $u: B\subset \mathbb{R}^2 \mapsto \mathbb{R}^2,$ $B$ being the unit disk, and subject to suitable boundary conditions. In the second part we focus on a very similar situations only exchanging the previous functionals by a suitable class of $p-$growing polyconvex functionals and allowing the maps to be arbitrary. In both cases a particular emphasis is laid on high pressure situations, where only uniqueness for a subclass, containing solely of variations with high enough Fourier-modes, can be obtained. |
| title | (High frequency)-uniqueness criteria for p-growth functionals in in- and compressible elasticity |
| topic | Analysis of PDEs 74G30, 74B20 |
| url | https://arxiv.org/abs/2210.12885 |