Operators in Morrey type spaces and applications

M. A. Ragusa

Eurasian mathematical journal, Tome 3 (2012) no. 3, pp. 94-109.

Résumé

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.

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