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arXiv · 1403.0428

Calder\'on problem for the p-Laplacian: First order derivative of conductivity on the boundary

Tommi Brander
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Abstract

We recover the gradient of a scalar conductivity defined on a smooth bounded open set in $\mathbb{R}^d$ from the Dirichlet to Neumann map arising from the $p$-Laplace equation. For any boundary point we recover the gradient using Dirichlet data supported on an arbitrarily small neighbourhood of the boundary point. We use a Rellich-type identity in the proof. Our results are new when $p \neq 2$. In the $p = 2$ case boundary determination plays a role in several methods for recovering the conductivity in the interior.

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Tommi Brander. 2014-03-03. Calder\'on problem for the p-Laplacian: First order derivative of conductivity on the boundary. https://doi.org/10.1090/proc/12681

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