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arXiv · 2512.01919

Dirichlet heat kernel estimates for parabolic nonlocal equations

Philipp Svinger·Marvin Weidner
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Abstract

In this article we establish the optimal $C^s$ boundary regularity for solutions to nonlocal parabolic equations in divergence form in $C^{1,\alpha}$ domains and prove a higher order boundary Harnack principle in this setting. Our approach applies to a broad class of nonlocal operators with merely H\"older continuous coefficients, but our results are new even in the translation invariant case. As an application, we obtain sharp two-sided estimates for the associated Dirichlet heat kernel. Notably, our estimates cover nonlocal operators with time-dependent coefficients, which had remained open in the literature.

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Philipp Svinger, Marvin Weidner. 2025-12-01. Dirichlet heat kernel estimates for parabolic nonlocal equations. https://arxiv.org/abs/2512.01919

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