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W1,p(·) regularity for quasilinear problems with irregular obstacles on Reifenberg domains

Authors: 

The Anh Bui, Xuan Truong Le*

Source title: 
Communications in Contemporary Mathematics, 19(6):1650046, 19 pages, 2017 (ISI)
Academic year of acceptance: 
2017-2018
Abstract: 

In this paper, we prove the global gradient estimates on the generalized Lebesgue spaces for weak solutions to elliptic quasilinear obstacle problems. It is worth noticing that the coefficients related to the obstacle problems are merely measurable with small BMO norms and the underlying domain does not satisfy any smoothness conditions.