Guido Stampacchia's paper addresses the Dirichlet problem for second-order elliptic equations with discontinuous coefficients. The operator under consideration is of divergence form, with measurable and bounded coefficients satisfying an ellipticity condition. The paper investigates the existence and properties of weak solutions to the Dirichlet problem, as well as the regularity of boundary points for the operator. It extends classical results from potential theory to more general elliptic operators, including those with lower-order terms. The author proves the maximum principle for weak solutions, establishes the continuity of solutions, and discusses the existence of Green's functions and potentials associated with the operator. The paper also introduces the concept of capacity for sets with respect to the operator and shows that regularity of boundary points is preserved under certain conditions. The results are applied to study the Dirichlet problem for a broader class of elliptic operators, including those with non-uniform coefficients. The paper concludes with a discussion of the relationship between the regularity of boundary points for the given operator and those for the Laplace operator.Guido Stampacchia's paper addresses the Dirichlet problem for second-order elliptic equations with discontinuous coefficients. The operator under consideration is of divergence form, with measurable and bounded coefficients satisfying an ellipticity condition. The paper investigates the existence and properties of weak solutions to the Dirichlet problem, as well as the regularity of boundary points for the operator. It extends classical results from potential theory to more general elliptic operators, including those with lower-order terms. The author proves the maximum principle for weak solutions, establishes the continuity of solutions, and discusses the existence of Green's functions and potentials associated with the operator. The paper also introduces the concept of capacity for sets with respect to the operator and shows that regularity of boundary points is preserved under certain conditions. The results are applied to study the Dirichlet problem for a broader class of elliptic operators, including those with non-uniform coefficients. The paper concludes with a discussion of the relationship between the regularity of boundary points for the given operator and those for the Laplace operator.