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Article Contents

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

• 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 $\frac{2n}{n+2} < p < 2.$

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

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