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.References
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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