Gradient estimate in Orlicz spaces for elliptic obstacle problems with partially BMO nonlinearities
Date
2018-03-01
Authors
Liang, Shuang
Zheng, Shenzhou
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Nonlinear elliptic obstacle problems, Partially BMO nonlinearities, Reifenberg flatness, Orlicz space, The Hardy-Littlewood maximal operator
Citation
Liang, S., & Zheng, S. (2018). Gradient estimate in Orlicz spaces for elliptic obstacle problems with partially BMO nonlinearities. <i>Electronic Journal of Differential Equations, 2018</i>(58), pp. 1-15.