L_p-estimates for solutions of second-order elliptic equation Dirichlet problem

摘要

For solutions of the Dirichlet problem for a second-order elliptic equation, we establish an analogue of the Carleson theorem on L_p-estimates. Under the same conditions on the coefficients for which the unique solvability of the considered problem is known, we prove this criterion for the validity of estimate of the solution norm in the space L_p with a measure. We require their Dini continuity on the boundary, but we assume only their measurability and boundedness in the domain under consideration.