Lower semicontinuity of weak supersolutions to the porous medium equation
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.
Main Authors
Format
Articles
Research article
Published
2015
Series
Subjects
Publication in research information system
Publisher
American Mathematical Society
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201509022788Use this for linking
Review status
Peer reviewed
ISSN
0002-9939
DOI
https://doi.org/10.1090/proc/12727
Language
English
Published in
Proceedings of the American Mathematical Society
Citation
- 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
License
Copyright© 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.