Calderón problem for the p-Laplace equation : First order derivative of conductivity on the boundary
Brander, T. (2016). Calderón problem for the p-Laplace equation : First order derivative of conductivity on the boundary. Proceedings of the American Mathematical Society, 144(1), 177-189. https://doi.org/10.1090/proc/12681
Published inProceedings of the American Mathematical Society
© 2015 American Mathematical Society. This is a final draft version of an article whose final and definitive form has been published by AMC. Published in this repository with the kind permission of the publisher.
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.
PublisherAmerican Mathematical Society
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