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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.01083 |
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| _version_ | 1866916853205434368 |
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| author | Brock, Friedemann Chiacchio, Francesco Croce, Gisella Mercaldo, Anna |
| author_facet | Brock, Friedemann Chiacchio, Francesco Croce, Gisella Mercaldo, Anna |
| contents | We study the shape of solutions to some variational problems in Sobolev spaces with weights that are powers of |x|. In particular, we detect situations when the extremal functions lack symmetry properties such as radial symmetry and antisymmetry. We also prove an isoperimetric inequality for the first non-zero eigenvalue of a weighted Neumann problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01083 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Shape of extremal functions for weighted Sobolev-type inequalities Brock, Friedemann Chiacchio, Francesco Croce, Gisella Mercaldo, Anna Optimization and Control We study the shape of solutions to some variational problems in Sobolev spaces with weights that are powers of |x|. In particular, we detect situations when the extremal functions lack symmetry properties such as radial symmetry and antisymmetry. We also prove an isoperimetric inequality for the first non-zero eigenvalue of a weighted Neumann problem. |
| title | Shape of extremal functions for weighted Sobolev-type inequalities |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2311.01083 |