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, are discussed some estimates for the derivatives of local minimizers of variational integrals.
Keywords and phrases:parabolic equation, Morrey spaces, well-posedness, discontinuous coefficients.
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