  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.
