Lower semicontinuity of weak supersolutions to the porous medium equation
Published inProceedings of the American Mathematical Society
© 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.