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arXiv · 1801.05249

Regularity of weak solutions and supersolutions to the porous medium equation

Verena Bögelein·Pekka Lehtelä·Stefan Sturm
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Abstract

We study the relations between different regularity assumptions in the definition of weak solutions and supersolutions to the porous medium equation. In particular, we establish the equivalence of the conditions $u^m \in L^2_{\rm loc}(0,T;H^1_{\rm loc}(\Omega))$ and $u^\frac{m+1}2 \in L^2_{\rm loc}(0,T;H^1_{\rm loc}(\Omega))$ in the definition of weak solutions. Our proof is based on approximation by solutions to obstacle problems.

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Verena Bögelein, Pekka Lehtelä, Stefan Sturm. 2018-01-16. Regularity of weak solutions and supersolutions to the porous medium equation. https://arxiv.org/abs/1801.05249

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