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J. reine angew. Math. 584 (2005), 117--148 Journal fur die reine und angewandte Mathematik
 

Summary: J. reine angew. Math. 584 (2005), 117--148 Journal fur die reine und
angewandte Mathematik
( Walter de Gruyter
Berlin New York 2005
Gradient estimates for the px-Laplacean system
By Emilio Acerbi and Giuseppe Mingione at Parma
Abstract. We prove Calderon and Zygmund type estimates for a class of elliptic
problems whose model is the non-homogeneous px-Laplacean system
divjDujpx2
Du divjFjpx2
F:
Under optimal continuity assumptions on the function px > 1 we prove that
jFjpx
A Lq
loc ) jDujpx
A Lq
loc Eq > 1:
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 Ruzicka [12] in the linear case.

  

Source: Acerbi, Emilio - Dipartimento di Matematica, Universit degli Studi di Parma

 

Collections: Mathematics