An inverse boundary value problem for the p-Laplacian: A linearization approach
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2019-01-28
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en
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Inverse Problems, Volume 35, issue 3
Abstract
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.Description
Keywords
Bayesian inversion, inverse boundary value problem, linearization, p-Laplacian
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Hannukainen, A, Hyvönen, N & Mustonen, L 2019, ' An inverse boundary value problem for the p-Laplacian : A linearization approach ', Inverse Problems, vol. 35, no. 3, 034001 . https://doi.org/10.1088/1361-6420/aaf2df