Regularity of weak solutions and supersolutions to the porous medium equation
| Autor: | Bögelein, Verena, Lehtelä, Pekka, Sturm, Stefan |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. |
| Databáze: | arXiv |
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