Weighted Orlicz regularity for fully nonlinear elliptic equations with oblique derivative at the boundary via asymptotic operators

We prove weighted Orlicz-Sobolev regularity for fully nonlin- ear elliptic equations with oblique boundary condition under asymptotic conditions of the following problem {F(D(2)u, Du, u, x) = f(x) in Omega beta. Du + gamma u = g on partial derivative Omega where Omega is a bounded domain in R-n(n >= 2), under suitable assumptions on the source term f, data beta, gamma and g. Our approach guarantees such estimates under conditions where the governing operator F does not require a convex (or concave) structure. We also deal with weighted Orlicz-type estimates for the obstacle problem with oblique derivative condition on the boundary. As a final application, the developed methods provide weighted Orlicz-BMO regularity for the Hessian, provided that the source lies in that space and in weighted Orlicz space associated. 2023 Elsevier Inc. All rights reserved.