An inverse boundary value problem for the p-Laplacian: a linearization approach

This work tackles an inverse boundary value problem for a p-Laplace type partial differential equation parametrized by a smoothening parameter . The aim is to numerically test reconstructing a conductivity type coefficient in the equation when Dirichlet boundary values of certain solutions to the corresponding Neumann problem serve as data. The numerical studies are based on a straightforward linearization of the forward map, and they demonstrate that the accuracy of such an approach depends nontrivially on and the chosen parametrization for the unknown coefficient. The numerical considerations are complemented by proving that the forward operator, which maps a Hölder continuous conductivity coefficient to the solution of the Neumann problem, is Fréchet differentiable, excluding the degenerate case that corresponds to the classical (weighted) -Laplace equation. (paper)