Enclosure method for the p-Laplace equation

Abstract

We study the enclosure method for the p-Calderón problem, which is a nonlinear generalization of the inverse conductivity problem due to Calderón 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.

20 pages, 2 figures

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• Reconstruction of piecewise constant layered conductivities in electrical impedance tomography
• Monotonicity Principle in Tomography of Nonlinear Conducting Materials
• The fractional $p$-biharmonic systems: optimal Poincaré constants, unique continuation and inverse problems
• Monotonicity-based reconstruction of extreme inclusions in electrical impedance tomography
• Inverse problems for $p$-Laplace type equations under monotonicity assumptions
• Imaging of nonlinear materials via the Monotonicity Principle
• New Development of the Enclosure Method for Inverse Obstacle Scattering
• The p-Laplace "Signature" for Quasilinear Inverse Problems with Large Boundary Data
• An inverse boundary value problem for the inhomogeneous porous medium equation
• The $p_0$-Laplace "Signature" for Quasilinear Inverse Problems
• The inverse obstacle problem for nonlinear inclusions
• Two uniqueness results in the inverse boundary value problem for the weighted p-Laplace equation