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Lower semicontinuity of weak supersolutions to the porous medium equation

Authors: Benny Avelin and Teemu Lukkari
Journal: Proc. Amer. Math. Soc. 143 (2015), 3475-3486
MSC (2010): Primary 35K55, 31C45
Published electronically: April 23, 2015
MathSciNet review: 3348790
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Abstract | References | Similar Articles | Additional Information

Abstract: Weak supersolutions to the porous medium equation are defined by means of smooth test functions under an integral sign. We show that nonnegative weak supersolutions become lower semicontinuous after redefinition on a set of measure zero. This shows that weak supersolutions belong to a class of supersolutions defined by a comparison principle.

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Additional Information

Benny Avelin
Affiliation: Department of Mathematics, Uppsala University, S-751 06 Uppsala, Sweden

Teemu Lukkari
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, 40014 Jyväskylä, Finland

Keywords: Porous medium equation, supersolutions, comparison principle, lower semicontinuity, degenerate diffusion
Received by editor(s): December 10, 2013
Published electronically: April 23, 2015
Additional Notes: The research reported in this work was done during the authors’ stay at the Institut Mittag-Leffler (Djursholm, Sweden).
Communicated by: Joachim Krieger
Article copyright: © Copyright 2015 American Mathematical Society

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