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

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 satisfies some measure condition at one boundary point, the bilinear mapping V, 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.