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arXiv · 2601.02863

Global Hölder Solvability of parabolic equations on domains with capacity density conditions

Takanobu Hara
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Abstract

We investigate the Cauchy-Dirichlet problem for linear parabolic equations in divergence form. Under mild assumptions on the source term and the domain, we prove the existence of globally Hölder continuous solutions. Notably, our results accommodate data exhibiting singularities nearly as critical as the inverse square of the distance from the boundary.

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Takanobu Hara. 2026-01-06. Global Hölder Solvability of parabolic equations on domains with capacity density conditions. https://arxiv.org/abs/2601.02863

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