A comparison principle for the porous medium equation and its consequences
Benny Avelin
Aalto University, Finland, and Uppsala Universitet, SwedenTeemu Lukkari
Aalto University, Finland
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Abstract
We prove a comparison principle for the porous medium equation in more general open sets in 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.
Cite this article
Benny Avelin, Teemu Lukkari, A comparison principle for the porous medium equation and its consequences. Rev. Mat. Iberoam. 33 (2017), no. 2, pp. 573–594
DOI 10.4171/RMI/950