Holder regularity for nonlocal in time subdiffusion equations with general kernel

Adam Kubica; Katarzyna Ryszewska; Rico Zacher

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arXiv · 2409.04841

Holder regularity for nonlocal in time subdiffusion equations with general kernel

Adam Kubica·Katarzyna Ryszewska·Rico Zacher

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Abstract

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.

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Adam Kubica, Katarzyna Ryszewska, Rico Zacher. 2024-09-07. Holder regularity for nonlocal in time subdiffusion equations with general kernel. https://arxiv.org/abs/2409.04841

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