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arXiv · 2405.04123

Two uniqueness results in the inverse boundary value problem for the weighted p-Laplace equation

Cătălin I. Cârstea·Ali Feizmohammadi
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Abstract

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.

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Cătălin I. Cârstea, Ali Feizmohammadi. 2024-05-07. Two uniqueness results in the inverse boundary value problem for the weighted p-Laplace equation. https://doi.org/10.1017/fms.2025.10095

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