The variationall Dirichlet problem with nonhomogeneous boundary conditions for degenerate elliptic operators

We study the variational Dirichlet problem with nonhomogeneous boundary conditions for degenerate elliptic operators in a bounded domain with summable lower coeficients in the case when the corresponding sesquilinear forms may not satisfy the coercivity condition. A case is singled out when nonhomogeneous boundary conditions are specified explicitly and their number depends on the degree of degeneration of the leading coeficients of the operator under study. An inequality is proved in which the norm of the solution of the nonhomogeneous variational Dirichlet problem is estimated from above by the norms of the boundary functions and the right-hand side of the equation.