Regularity and existence results for degenerate elliptic operators

In the first section of this paper we study the Holder-continuity of solutions of the Schrodinger degenerate equation -Sigma(n)(i,j=1) (a(if)u(x1))(xj) + cu = 0, (*) assuming the potential c belonging to appropriate degenerate Morrey spaces. In the second section we obtain the existence and the uniqueness of the solution of a variational inequality associated to the degenerate operator Lu = -Sigma(n)(i,j-1) (a(ij) (x)u(xi) + d(j)u)(xj) + Sigma(i=1)(n)b(i)u(xi) + cu (**) assuming the coefficients of the lower terms and the known term belonging to a suitable degenerate Stummel-Kato class. In both cases the weight w, which gives the degeneration, belongs to the Muckenoupt class A(2.)