Calderón problem for the p-Laplacian: First order derivative of conductivity on the boundary

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 $p\ne 2$. In the $p=2$ case boundary determination plays a role in several methods for recovering the conductivity in the interior.

12 pages. Minor corrections and added references

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