Enclosure method for the p-Laplace equation
Brander, T., Kar, M., & Salo, M. (2015). Enclosure method for the p-Laplace equation. Inverse Problems, 31(4), Article 045001. https://doi.org/10.1088/0266-5611/31/4/045001
Published inInverse Problems
DisciplineMatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse Problems
© Institute of Physics Publishing Ltd. and Institute of Physics 2015. This is a final draft version of an article whose final and definitive form has been published by Institute of Physics Publishing Ltd. and Institute of Physics.
Abstract. We study the enclosure method for the p-Calderon problem, which is a nonlinear generalization of the inverse conductivity problem due to Calderon that involves the p-Laplace equation. The method allows one to reconstruct the convex hull of an inclusion in the nonlinear model by using exponentially growing solutions introduced by Wolff. We justify this method for the penetrable obstacle case, where the inclusion is modelled as a jump in the conductivity. The result is based on a monotonicity inequality and the properties of the Wolff solutions.
PublisherInstitute of Physics Publishing Ltd.; Institute of Physics
Publication in research information system
MetadataShow full item record
Showing items with similar title or keywords.
Brander, Tommi; Harrach, Bastian; Kar, Manas; Salo, Mikko (Society for Industrial and Applied Mathematics, 2018)We show that the convex hull of a monotone perturbation of a homogeneous background conductivity in the p-conductivity equation is determined by knowledge of the nonlinear Dirichlet--Neumann operator. We give two independent ...
Brander, Tommi (University of Jyväskylä, 2016)We investigate a generalization of Calderón’s problem of recovering the conductivity coeﬃcient in a conductivity equation from boundary measurements. As a model equation we consider the p-conductivity equation div σ ...
Guo, Changyu; Kar, Manas; Salo, Mikko (EUT Edizioni Universita di Trieste, 2016)We consider inverse problems for p-Laplace type equations under monotonicity assumptions. In two dimensions, we show that any two conductivities satisfying σ1 ≥ σ2 and having the same nonlinear Dirichlet-to-Neumann map ...
Calderón problem for the p-Laplace equation : First order derivative of conductivity on the boundary Brander, Tommi (American Mathematical Society, 2016)We recover the gradient of a scalar conductivity defined on a smooth bounded open set in Rd from the Dirichlet to Neumann map arising from the p-Laplace equation. For any boundary point we recover the gradient using Dirichlet ...
Brander, Tommi; Ilmavirta, Joonas; Kar, Manas (American Institute of Mathematical Sciences, 2018)We detect an inclusion with infinite conductivity from boundary measurements represented by the Dirichlet-to-Neumann map for the conductivity equation. We use both the enclosure method and the probe method. We use the ...