Two uniqueness results in the inverse boundary value problem for the weighted p-Laplace equation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916949343076352 |
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| author | Cârstea, Cătălin I. Feizmohammadi, Ali |
| author_facet | Cârstea, Cătălin I. Feizmohammadi, Ali |
| contents | In this paper we prove a general uniqueness result in the inverse boundary value problem for the weighted p-Laplace equation in the plane, with smooth weights. We also prove a uniqueness result in dimension 3 and higher, for real analytic weights that are subject to a smallness condition on one of their directional derivatives. Both results are obtained by linearizing the equation at a solution without critical points. This unknown solution is then recovered, together with the unknown weight. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_04123 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two uniqueness results in the inverse boundary value problem for the weighted p-Laplace equation Cârstea, Cătălin I. Feizmohammadi, Ali Analysis of PDEs In this paper we prove a general uniqueness result in the inverse boundary value problem for the weighted p-Laplace equation in the plane, with smooth weights. We also prove a uniqueness result in dimension 3 and higher, for real analytic weights that are subject to a smallness condition on one of their directional derivatives. Both results are obtained by linearizing the equation at a solution without critical points. This unknown solution is then recovered, together with the unknown weight. |
| title | Two uniqueness results in the inverse boundary value problem for the weighted p-Laplace equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.04123 |