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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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Parabolic comparison principle and quasiminimizers in metric measure spaces
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by Juha Kinnunen and Mathias Masson PDF
Proc. Amer. Math. Soc. 143 (2015), 621-632 Request permission

Abstract:

We give several characterizations of parabolic (quasisuper)- minimizers in a metric measure space equipped with a doubling measure and supporting a Poincaré inequality. We also prove a version of comparison principle for super- and subminimizers on parabolic space-time cylinders and a uniqueness result for minimizers of a boundary value problem. We also give an example showing that the corresponding results do not hold, in general, for quasiminimizers even in the Euclidean case.
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Additional Information
  • Juha Kinnunen
  • Affiliation: Department of Mathematics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland
  • MR Author ID: 349676
  • Email: juha.k.kinnunen@aalto.fi
  • Mathias Masson
  • Affiliation: Department of Mathematics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland
  • Email: mathiasmasson@hotmail.com
  • Received by editor(s): January 11, 2013
  • Received by editor(s) in revised form: April 10, 2013
  • Published electronically: November 3, 2014
  • Communicated by: Joachim Krieger
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 621-632
  • MSC (2010): Primary 30L99, 35K92
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12236-2
  • MathSciNet review: 3283649