Electron. J. Differential Equations, Vol. 2018 (2018), No. 58, pp. 1-15.

Gradient estimate in Orlicz spaces for elliptic obstacle problems with partially BMO nonlinearities

Shuang Liang, Shenzhou Zheng

Abstract:
We prove a global Orlicz estimate for the gradient of weak solutions to a class of nonlinear obstacle problems with partially regular nonlinearities in nonsmooth domains. It is assumed that the nonlinearities are merely measurable in one spatial variable and have sufficiently small BMO semi-norm in the other variables, and the boundary of underlying domain is Reifenberg flat.

Submitted October 2, 2017. Published March 1, 2018.
Math Subject Classifications: 35D30, 35K10.
Key Words: Nonlinear elliptic obstacle problems; partially BMO nonlinearities; Reifenberg flatness; Orlicz space; the Hardy-Littlewood maximal operator.

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Shuang Liang
Department of Mathematics
Beijing Jiaotong University
Beijing 100044, China
email: shuangliang@bjtu.edu.cn
Shenzhou Zheng
Department of Mathematics
Beijing Jiaotong University
Beijing 100044, China
email: shzhzheng@bjtu.edu.cn

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