Holder regularity for nonlocal in time subdiffusion equations with general kernel
| Autor: | Kubica, Adam, Ryszewska, Katarzyna, Zacher, Rico |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We study the regularity of weak solutions to nonlocal in time subdiffusion equations for a wide class of weakly singular kernels appearing in the generalised fractional derivative operator. We prove a weak Harnack inequality for nonnegative weak supersolutions and Holder continuity of weak solutions to such problems. Our results substantially extend the results from our previous work [12] by leaving the framework of distributed order fractional time derivatives and considering a general PC kernel and by also allowing for an inhomogeneity in the PDE from a Lebesgue space of mixed type. Comment: 52 pages |
| Databáze: | arXiv |
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