Year: 2024
Type: preprint
Abstract: In this paper I consider the inverse boundary value problem for a quasilinear, anisotropic, elliptic equation of the form $\nabla\cdot(γ\nabla u+|\nabla u|^{p-2}\nabla u)=0$, where $γ$ is a smooth, matrix valued, function with a uniform lower bound. I show that boundary Dirichlet and Neumann data for this equation, in the form of a Dirichlet-to-Neumann map, determine the coefficient matrix uniquely, in dimension 3 and higher. This stands in contrast to the classical linear anisotropic Calderón problem where there is a known obstruction to uniqueness due to the invariance of the boundary data under transformations of the equation via any boundary fixing diffeomorphism.
Source: arXiv (Cornell University)
Author: Cârstea, Cătălin I.
Institution: National Yang Ming Chiao Tung University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4399990921