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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Calderón problem for the $p$-Laplacian: First order derivative of conductivity on the boundary
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by Tommi Brander PDF
Proc. Amer. Math. Soc. 144 (2016), 177-189 Request permission

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 $p \neq 2$. In the $p=2$ case boundary determination plays a role in several methods for recovering the conductivity in the interior.
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Additional Information
  • Tommi Brander
  • Affiliation: Department of Mathematics and Statistics, P.O. Box 35 (MaD) FI-40014 University of Jyväskylä, Finland
  • Email: tommi.o.brander@jyu.fi
  • Received by editor(s): March 4, 2014
  • Received by editor(s) in revised form: November 26, 2014
  • Published electronically: July 24, 2015
  • Communicated by: Joachim Krieger
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 177-189
  • MSC (2010): Primary 35R30, 35J92
  • DOI: https://doi.org/10.1090/proc/12681
  • MathSciNet review: 3415587