The estimates of the solution of the Dirichlet problem with boundary function from $L_p$ for a second-order elliptic equation

We study the solvability of the Dirichlet problem for a second-order elliptic equation with measurable and bounded coefficients. Assuming that coefficients of equation are Dini-continued on the boundary, it is established that there is the unique solution of the Dirichlet problem with boundary function from $L_p$, $p>1$. We prove the estimate of the analogue of area integral.