6533b85cfe1ef96bd12bccf4

RESEARCH PRODUCT

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

Tommi Brander

subject

Calderón problemp-LaplacianMathematics::Spectral Theory

description

We recover the gradient of a scalar conductivity defined on a smooth bounded open set in Rd 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 6 = 2. In the p = 2 case boundary determination plays a role in several methods for recovering the conductivity in the interior. peerReviewed

http://urn.fi/URN:NBN:fi:jyu-201510273516