Global H\"{o}lder Solvability of parabolic equations on domains with capacity density conditions

Takanobu Hara

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arXiv · 2601.02863

Global H\"{o}lder 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 H\"{o}lder 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 H\"{o}lder Solvability of parabolic equations on domains with capacity density conditions. https://arxiv.org/abs/2601.02863

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