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Main Authors: Jingqi, Liang, Lihe, Wang, Chunqin, Zhou
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2408.01073
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author Jingqi, Liang
Lihe, Wang
Chunqin, Zhou
author_facet Jingqi, Liang
Lihe, Wang
Chunqin, Zhou
contents In this paper, we prove the boundary pointwise $C^{0}$-regularity of weak solutions for Dirichlet problem of elliptic equations in divergence form with distributional coefficients, where the boundary value equals to zero. This is a generalization of the interior case. If $Ω$ satisfies some measure condition at one boundary point, the bilinear mapping $\langle V\cdot,\cdot\rangle$ generalized by distributional coefficient $V$ can be controlled by a constant sufficiently small, the nonhomogeneous terms satisfy some Dini decay conditions, then the solution is continuous at this point in the $L^{2}$ sense.
format Preprint
id arxiv_https___arxiv_org_abs_2408_01073
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Boundary C^α-regularity for solutions of elliptic equations with distributional coefficients
Jingqi, Liang
Lihe, Wang
Chunqin, Zhou
Analysis of PDEs
In this paper, we prove the boundary pointwise $C^{0}$-regularity of weak solutions for Dirichlet problem of elliptic equations in divergence form with distributional coefficients, where the boundary value equals to zero. This is a generalization of the interior case. If $Ω$ satisfies some measure condition at one boundary point, the bilinear mapping $\langle V\cdot,\cdot\rangle$ generalized by distributional coefficient $V$ can be controlled by a constant sufficiently small, the nonhomogeneous terms satisfy some Dini decay conditions, then the solution is continuous at this point in the $L^{2}$ sense.
title Boundary C^α-regularity for solutions of elliptic equations with distributional coefficients
topic Analysis of PDEs
url https://arxiv.org/abs/2408.01073