Boundary C^{\alpha}-regularity for solutions of elliptic equations with distributional coefficients

Liang Jingqi; Wang Lihe; Zhou Chunqin

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arXiv · 2408.01073

Boundary C^{\alpha}-regularity for solutions of elliptic equations with distributional coefficients

Liang Jingqi·Wang Lihe·Zhou Chunqin

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Abstract

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 $\Omega$ 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.

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Liang Jingqi, Wang Lihe, Zhou Chunqin. 2024-08-02. Boundary C^{\alpha}-regularity for solutions of elliptic equations with distributional coefficients. https://arxiv.org/abs/2408.01073

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