Regular boundary points and the Dirichlet problem for elliptic equations in double divergence form

We study the Dirichlet problem for a second-order elliptic operator $L^{\ast }$ in double divergence form, also known as the stationary Fokker-Planck-Kolmogorov equation. Assuming that the leading coefficients have Dini mean oscillation, we establish the equivalence between regular boundary points for the operator $L^{\ast }$ and those for the Laplace operator, as characterized by the classical Wiener criterion.