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Abstract
This work tackles an inverse boundary value problem for a pLaplace 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.
Original language  English 

Article number  034001 
Journal  Inverse Problems 
Volume  35 
Issue number  3 
DOIs  
Publication status  Published  28 Jan 2019 
MoE publication type  A1 Journal articlerefereed 
Keywords
 Bayesian inversion
 inverse boundary value problem
 linearization
 pLaplacian
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Dive into the research topics of 'An inverse boundary value problem for the pLaplacian: A linearization approach'. Together they form a unique fingerprint.Projects
 2 Finished

Centre of Excellence of Inverse Modelling and Imaging
Hannukainen, A., Kuutela, T., Ojalammi, A., Kuortti, J. & Puska, J.
01/01/2018 → 31/12/2020
Project: Academy of Finland: Other research funding

Centre of Excellence of Inverse Modelling and Imaging
Ojalammi, A., Hyvönen, N., Hirvi, P., Kuutela, T. & Puska, J.
01/01/2018 → 31/12/2020
Project: Academy of Finland: Other research funding