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An inverse boundary value problem for the p -Laplacian: a linearization approach by Antti Hannukainen; Nuutti Hyvönen; Lauri Mustonen is a Engineering article available to read on EtoBox.

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This work tackles an inverse boundary value problem for a p-Laplace type partial differential equation parametrized by a smoothening parameter τ ≥ 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 τ = 0 that corresponds to the classical (weighted) p-Laplace equation.

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Author

Antti Hannukainen; Nuutti Hyvönen; Lauri Mustonen

Publisher

IOP Publishing

Published

2019

Language

EN

Field

Engineering (Physical Sciences)