An inverse boundary value problem for the p-Laplacian: A linearization approach
Research output: Contribution to journal › Article
- Stanford University
This work tackles an inverse boundary value problem for a p-Laplace type partial differential equation parametrized by a smoothening parameter T ≥ 0. 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 1 < p < ∞ 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 T = 0 that corresponds to the classical (weighted) -Laplace equation.
|Publication status||Published - 28 Jan 2019|
|MoE publication type||A1 Journal article-refereed|
- Bayesian inversion, inverse boundary value problem, linearization, p-Laplacian