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Title: On very weak solutions of a class of nonlinear elliptic systems (English)
Author: Carozza, Menita
Author: Passarelli di Napoli, Antonia
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 41
Issue: 3
Year: 2000
Pages: 493-508
Category: math
Summary: In this paper we prove a regularity result for very weak solutions of equations of the type $- \operatorname{div} A(x,u,Du)=B(x, u,Du)$, where $A$, $B$ grow in the gradient like $t^{p-1}$ and $B(x, u, Du)$ is not in divergence form. Namely we prove that a very weak solution $u\in W^{1,r}$ of our equation belongs to $W^{1,p}$. We also prove global higher integrability for a very weak solution for the Dirichlet problem $$ \cases -\operatorname{div} A(x,u,Du)\,=B(x, u,Du) \quad & \text{in } \Omega , \ u-u_o\in W^{1,r}(\Omega,\Bbb R^m). \endcases $$ (English)
Keyword: nonlinear elliptic systems
Keyword: maximal operator theory
MSC: 35B65
MSC: 35D05
MSC: 35J50
MSC: 35J55
MSC: 35J60
MSC: 35J99
MSC: 46E30
idZBL: Zbl 1119.35016
idMR: MR1795081
Date available: 2009-01-08T19:04:34Z
Last updated: 2012-04-30
Stable URL:
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