Higher integrability results for non smooth parabolic systems: The subquadratic case

Chiara Leone; Anna Verde; Giovanni Pisante

doi:10.3934/dcdsb.2009.11.177

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2009, Volume 11, Issue 1: 177-190. Doi: 10.3934/dcdsb.2009.11.177

This issue Previous Article The Janossy effect and hybrid variational principles Next Article Existence of bounded solutions to some nonlinear degenerate elliptic systems

Higher integrability results for non smooth parabolic systems: The subquadratic case

1.
Dipartimento di Matematica e Applicazioni, Università degli Studi “Federico II” di Napoli, via Cinthia - Monte S. Angelo - 80126 Napoli
2.
Dipartimento di Matematica, Seconda Università degli Studi di Napoli, via Vivaldi 43 - 81100 Caserta

Received: November 30, 2007

Revised: May 31, 2008

Published: June 2009

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Abstract

In this paper we deal with the study of some regularity properties of weak solutions to non-linear, second-order parabolic systems of the type

$ u_{t}-$div$A(Du)=0, $ $ (x,t)\in \Omega \times (0,T)=\Omega_{T}, $

where $\Omega \subset \mathbb{R}^{n}$ is a bounded domain, $T>0$, $A:\mathbb{R}^{nN}\to \mathbb{R}^{N}$ satisfies a $p$-growth condition and $u:\Omega_{T}\to \mathbb{R}^{N}$. In particular we focus on the case $\frac{2n}{n+2} < p < 2.$

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Mathematics Subject Classification: 35K10, 35K55, 35D10, 35D10, 35B65.

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