Gradient estimates for the p (x)-Laplacean system

Abstract We prove Calderón and Zygmund type estimates for a class of elliptic problems whose model is the non-homogeneous p (x )-Laplacean system Under optimal continuity assumptions on the function p (x ) > 1 we prove that Our estimates are motivated by recent developments in non-Newtonian fluidmechanics and elliptic problems with non-standard growth conditions, and are the natural, ‘‘non-linear’’ counterpart of those obtained by Diening and Růžička [L. Diening and M. Růžička, Calderón-Zygmund operators on generalized Lebesgue spaces L p (‧) and problems related to fluid dynamics, J. reine angew. Math. 563 (2003), 197–220] in the linear case.

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