Uniformly Elliptic Equations on Domains with Capacity Density Conditions: Existence of Hölder Continuous Solutions and Homogenization Results

2024/10/23 by Takanobu Hara, Hara, Takanobu
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2410.18327

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 Hölder continuous solutions. Additionally, we apply the result to homogenization problems of ε-periodic coefficients and present a convergence rate estimate of L^∞ norms.

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