Inverse problems for $p$-Laplace type equations under monotonicity assumptions

Chang-Yu Guo; Manas Kar; Mikko Salo

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arXiv · 1602.02591

Inverse problems for $p$-Laplace type equations under monotonicity assumptions

Chang-Yu Guo·Manas Kar·Mikko Salo

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Abstract

We consider inverse problems for $p$-Laplace type equations under monotonicity assumptions. In two dimensions, we show that any two conductivities satisfying $\sigma_1 \geq \sigma_2$ and having the same nonlinear Dirichlet-to-Neumann map must be identical. The proof is based on a monotonicity inequality and the unique continuation principle for $p$-Laplace type equations. In higher dimensions, where unique continuation is not known, we obtain a similar result for conductivities close to constant.

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Chang-Yu Guo, Manas Kar, Mikko Salo. 2016-02-08. Inverse problems for $p$-Laplace type equations under monotonicity assumptions. https://arxiv.org/abs/1602.02591

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