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

We recover the gradient of a scalar conductivity defined on a smooth bounded open set in R d R^d from the Dirichlet to Neumann map arising from the p 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 ≠ 2 p ≠ 2 . In the p = 2 p=2 case boundary determination plays a role in several methods for recovering the conductivity in the interior.