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A comparison principle for the porous medium equation and its consequences
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.ORCID iD: 0000-0002-1429-4965
Aalto Univ, Finland.
2017 (English)In: Revista matemática iberoamericana, ISSN 0213-2230, E-ISSN 2235-0616, Vol. 33, no 2, 573-594 p.Article in journal (Refereed) Published
Abstract [en]

We prove a comparison principle for the porous medium equation in more general open sets in Rn+1 than space-time cylinders. We apply this result in two related contexts: we establish a connection between a potential theoretic notion of the obstacle problem and a notion based on a variational inequality. We also prove the basic properties of the PME capacity, in particular that there exists a capacitary extremal which gives the capacity for compact sets.

Place, publisher, year, edition, pages
2017. Vol. 33, no 2, 573-594 p.
Keyword [en]
Porous medium equation, PME, elliptic comparison principle, obstacle problem, parabolic capacity
National Category
Mathematical Analysis Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-329153DOI: 10.4171/RMI/950ISI: 000403582900009OAI: oai:DiVA.org:uu-329153DiVA: diva2:1141685
Funder
Swedish Research Council, 637-2014-6822
Available from: 2017-09-15 Created: 2017-09-15 Last updated: 2017-09-15Bibliographically approved

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Avelin, Benny

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