Higher integrability for doubly nonlinear parabolic systems

TL;DR

This paper establishes a local higher integrability property for the spatial gradient of weak solutions to doubly nonlinear parabolic systems, using an innovative approach that incorporates the solution and its gradient into the geometric analysis.

Contribution

It introduces a novel method involving intrinsic geometry that depends on both the solution and its gradient, extending higher integrability results to a broader class of nonlinear systems.

Findings

Proves higher integrability for the gradient of solutions.

Valid for a wide range of parameters.

Employs a new geometric approach involving the solution itself.

Abstract

This paper proves a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems. The new feature of the argument is that the intrinsic geometry involves the solution as well as its spatial gradient. The main result holds true for a range of parameters suggested by other nonlinear parabolic systems.