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arXiv · 2410.18327

Uniformly Elliptic Equations on Domains with Capacity Density Conditions: Existence of H\"{o}lder Continuous Solutions and Homogenization Results

Takanobu Hara
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Abstract

This is a progress report on study of uniformly elliptic Poisson-type equations on domains with capacity density conditions (CDC domains). We give a brief summary of known facts of CDC domains, including Hardy's inequality, and review a previous work of existence of globally H\"{o}lder continuous solutions. Additionally, we apply the result to homogenization problems of $\epsilon$-periodic coefficients and present a convergence rate estimate of $L^{\infty}$ norms.

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Takanobu Hara. 2024-10-23. Uniformly Elliptic Equations on Domains with Capacity Density Conditions: Existence of H\"{o}lder Continuous Solutions and Homogenization Results. https://arxiv.org/abs/2410.18327

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