Electron. J. Differential Equations, Vol. 2020 (2020), No. 13, pp. 1-25.

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

Hong Tian, Shenzhou Zheng

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.
DOI: 10.58997/ejde.2020.13

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Hong Tian
College of Science
Tianjin University of Technology
Tianjin 300384, China
email: 14118404@bjtu.edu.cn
Shenzhou Zheng
Department of Mathematics
Beijing Jiaotong University
Beijing 100044, China
email: shzhzheng@bjtu.edu.cn

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