Calderón problem for the p-Laplace equation : 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 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.
Main Author
Format
Articles
Research article
Published
2016
Series
Subjects
Publication in research information system
Publisher
American Mathematical Society
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201510273516Use this for linking
Review status
Peer reviewed
ISSN
0002-9939
DOI
https://doi.org/10.1090/proc/12681
Language
English
Published in
Proceedings of the American Mathematical Society
Citation
- 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
License
Copyright© 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.