Higher integrability for anisotropic parabolic systems of p-Laplace type

Abstract

In this article, we consider anisotropic parabolic systems of pp-Laplace type. The model case is the parabolic pi{p}_{i}-Laplace system ut−∑i=1n∂∂xi(∣Diu∣pi−2Diu)=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 pi≥2{p}_{i}\ge 2. Under the assumption that the exponents are not too far apart, i.e., the difference pmax−pmin{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.

Keywords

• finite differences
• higher integrability
• parabolic systems
• primary: 35k40
• secondary: 35b65