English

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

Analysis of PDEs 2025-09-16 v1

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.

Keywords

Cite

@article{arxiv.2405.04123,
  title  = {Two uniqueness results in the inverse boundary value problem for the weighted p-Laplace equation},
  author = {Cătălin I. Cârstea and Ali Feizmohammadi},
  journal= {arXiv preprint arXiv:2405.04123},
  year   = {2025}
}