Lower semicontinuity of weak supersolutions to the porous medium equation
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
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.
Porous medium equation, supersolutions, comparison principle, lower semicontinuity, degenerate diffusion
IdentifiersURN: urn:nbn:se:uu:diva-259086DOI: 10.1090/proc/12727ISI: 000357042200028OAI: oai:DiVA.org:uu-259086DiVA: diva2:843516