Projects per year
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
Fingerprint
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., Kuortti, J., Perkkiö, L., Ojalammi, A. & Puska, J.
01/01/2018 → 31/12/2020
Project: Academy of Finland: Other research funding

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