A suitable description of the weak closure of feasible states is given for the family of equations divA(x)del u = f(x) in Omega, u is an element of H-0(1)(Omega), Omega subset of R-n, with A is an element of M, where the set M consists of all measurable symmetric matrices whose eigenvalues at almost every x is an element of Omega belong to a given finite set {(lambda(1)(1) 1 1, ...,lambda(n)(1));...; (lambda(1)(N),...,lambda(n)(N))} subset of R-n and which satisfy additional constraints on the measure of sets where the eigenvalues of A are equal to some (lambda(1)(i),...,lambda(n)(i)); i = 1,..., N. Applications to optimal control problems are also considered.