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arXiv · 1505.07579

A comparison principle for the porous medium equation and its consequences

Benny Avelin·Teemu Lukkari
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Abstract

We prove a comparison principle for the porous medium equation in more general open sets in $\mathbb{R}^{n+1}$ 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.

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Benny Avelin, Teemu Lukkari. 2015-09-15. A comparison principle for the porous medium equation and its consequences. https://doi.org/10.4171/rmi%2F950

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