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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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Gradient estimates for the p (x)-Laplacean system

Emilio Acerbi1 / Giuseppe Mingione2

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2.

Citation Information: Journal für die reine und angewandte Mathematik. Volume 2005, Issue 584, Pages 117–148, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crll.2005.2005.584.117, November 2005

Publication History

Received:
6. Mai 2004
Published Online:
2005-11-07

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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