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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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On the mean value property for the $p$-Laplace equation in the plane
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by Peter Lindqvist and Juan Manfredi PDF
Proc. Amer. Math. Soc. 144 (2016), 143-149 Request permission

Abstract:

We study the $p$-Laplace equation in the plane and prove that the mean value property holds directly for the solutions themselves for $1<p<9.525...$. This removes the need to interpret the formula in the viscosity sense via test functions. The method is based on the hodograph representation.
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Additional Information
  • Peter Lindqvist
  • Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491, Trondheim, Norway
  • MR Author ID: 114355
  • Juan Manfredi
  • Affiliation: Office of the Provost, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
  • MR Author ID: 205679
  • Received by editor(s): November 2, 2014
  • Received by editor(s) in revised form: November 18, 2014
  • Published electronically: May 28, 2015

  • Dedicated: To the memory of our friend Albert Baernstein II
  • Communicated by: Jeremy T. Tyson
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 143-149
  • MSC (2010): Primary 35J92, 35J62
  • DOI: https://doi.org/10.1090/proc/12675
  • MathSciNet review: 3415584