Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 13, pp. 1-25.

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

Authors: Hong Tian (Tianjin Univ. of Technology, Tianjin, China)
         Shenzhou Zheng (Beijing Jiaotong Univ., Beijing, China)

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.
 
Submitted August 21, 2019. Published January 27, 2020.
Math Subject Classifications: 35B65, 35K86, 46E30.
Key Words: Parabolic obstacle problems; discontinuous nonlinearities;
           p(t,x)-growth; Orlicz spaces; Reifenberg flat domains.