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Parabolic comparison principle and quasiminimizers in metric measure spaces


Authors: Juha Kinnunen and Mathias Masson
Journal: Proc. Amer. Math. Soc. 143 (2015), 621-632
MSC (2010): Primary 30L99, 35K92
Published electronically: November 3, 2014
MathSciNet review: 3283649
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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
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

DOI: https://doi.org/10.1090/S0002-9939-2014-12236-2
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.