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

Abstract

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 Lp, p>1. We prove the estimate of the analogue of area integral.