Boundary C^α-regularity for solutions of elliptic equations with distributional coefficients

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 $⟨V\cdot ,\cdot ⟩$ 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.