# American Institute of Mathematical Sciences

January  2009, 11(1): 177-190. doi: 10.3934/dcdsb.2009.11.177

## 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, Italy, Italy 2 Dipartimento di Matematica, Seconda Università degli Studi di Napoli, via Vivaldi 43 - 81100 Caserta, Italy

Received  December 2007 Revised  June 2008 Published  November 2008

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 $\frac{2n}{n+2} < p < 2.$

Citation: Chiara Leone, Anna Verde, Giovanni Pisante. Higher integrability results for non smooth parabolic systems: The subquadratic case. Discrete and Continuous Dynamical Systems - B, 2009, 11 (1) : 177-190. doi: 10.3934/dcdsb.2009.11.177
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