Orlicz estimates for general parabolic obstacle problems with p(t,x)-growth in Reifenberg domains

Abstract

This article shows a global gradient estimate in the framework of Orlicz spaces for general parabolic obstacle problems with p(t,x)-Laplacian in a bounded rough domain. It is assumed that the variable exponent p(t,x) satisfies a strong log-Holder continuity, that the associated nonlinearity is measurable in the time variable and have small BMO semi-norms in the space variables, and that the boundary of the domain has Reifenberg flatness.

Keywords

• parabolic obstacle problems
• discontinuous nonlinearities
• p(t,x)-growth
• orlicz spaces
• reifenberg flat domains