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

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.

Keywords

• Nonlinear elliptic obstacle problems
• partially BMO nonlinearities
• Reifenberg flatness
• Orlicz space
• the Hardy-Littlewood maximal operator