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Lower semicontinuity of weak supersolutions to the porous medium equation
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2015 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 143, no 8, 3475-3486 p.Article in journal (Refereed) Published
Abstract [en]

Weak supersolutions to the porous medium equation are defined by means of smooth test functions under an integral sign. We show that non-negative 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.

Place, publisher, year, edition, pages
2015. Vol. 143, no 8, 3475-3486 p.
Keyword [en]
Porous medium equation, supersolutions, comparison principle, lower semicontinuity, degenerate diffusion
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-259086DOI: 10.1090/proc/12727ISI: 000357042200028OAI: oai:DiVA.org:uu-259086DiVA: diva2:843516
Available from: 2015-07-29 Created: 2015-07-27 Last updated: 2017-12-04Bibliographically approved

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Avelin, Benny

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