Lower semicontinuity of weak supersolutions to the porous medium equation
Avelin, B., & Lukkari, T. (2015). Lower semicontinuity of weak supersolutions to the porous medium equation. Proceedings of the American Mathematical Society, 143(8), 3475-3486. https://doi.org/10.1090/proc/12727
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Proceedings of the American Mathematical SocietyDate
2015Copyright
© 2015 American Mathematical Society. This is a final draft version of an article whose final and definitive form has been published by AMS. Published in this repository with the kind permission of the publisher.
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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American Mathematical SocietyISSN Search the Publication Forum
0002-9939Keywords
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