Higher integrability for anisotropic parabolic systems of p-Laplace type

Abstract

Abstract In this article, we consider anisotropic parabolic systems of p p -Laplace type. The model case is the parabolic p i {p}_{i} -Laplace system u t − ∑ i = 1 n ∂ ∂ x i ( ∣ D i u ∣ p i − 2 D i u ) = 0 {u}_{t}-\mathop{\sum }\limits_{i=1}^{n}\frac{\partial }{\partial {x}_{i}}({| {D}_{i}u| }^{{p}_{i}-2}{D}_{i}u)=0 with exponents p i ≥ 2 {p}_{i}\ge 2 . Under the assumption that the exponents are not too far apart, i.e., the difference p max − p min {p}_{\max }-{p}_{\min } is sufficiently small, we establish a higher integrability result for weak solutions. This extends a result, which was only known for the elliptic setting, to the parabolic setting.