An inverse problem for the p-Laplacian: boundary determination

Mikko Salo; Xiao Zhong

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arXiv · 1106.4229

An inverse problem for the p-Laplacian: boundary determination

Mikko Salo·Xiao Zhong

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Abstract

We study an inverse problem for nonlinear elliptic equations modelled after the p-Laplacian. It is proved that the boundary values of a conductivity coefficient are uniquely determined from boundary measurements given by a nonlinear Dirichlet-to-Neumann map. The result is constructive and local, and gives a method for determining the coefficient at a boundary point from measurements in a small neighborhood. The proofs work with the nonlinear equation directly instead of being based on linearization. In the complex valued case we employ complex geometrical optics type solutions based on p-harmonic exponentials, while for the real case we use p-harmonic functions first introduced by Wolff.

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Mikko Salo, Xiao Zhong. 2011-06-21. An inverse problem for the p-Laplacian: boundary determination. https://arxiv.org/abs/1106.4229

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