Operators in Morrey type spaces and applications

Abstract

We consider partial differential equations with discontinuous coefficients and prove that, if the known term belongs to the Morrey space \( L^{p,\lambda} \), the highest order derivatives of the solutions of the equations belong to the same space. As a consequence it is possible to obtain local Hölder continuity for the solutions. Moreover, some estimates for the derivatives of local minimizers of variational integrals are discussed.