Higher integrability results for non smooth parabolic systems: The subquadratic case
Chiara Leone, Anna Verde, Giovanni Pisante · Discrete and Continuous Dynamical Systems - B · 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, $T>0$, $A:\mathbb{R}^{nN}\to \mathbb{R}^{N}$ satisfiesa $p$-growth condition and $u:\Omega_{T}\to \mathbb{R}^{N}$. In particular we focus on the case $\frac{2n}{n+2} < p < 2.$