Global weighted Lorentz estimates of oblique tangential derivative problems for weakly convex fully nonlinear operators

Abstract

In this work, we develop weighted Lorentz-Sobolev estimates for viscosity solutions of fully nonlinear elliptic equations with oblique boundary condition under weakened convexity conditions in the following configuration $F(D^{2}u, Du, u, x) = f(x)$ in $\Omega$ and $\beta\cdot Du+\gamma u=g$ on $\partial \Omega$, where $\Omega$ is a bounded domain in $\mathbb{R}^{n}$ ($n \geq 2$), under suitable assumptions on the source term f, data $\beta$, $\gamma$ and g. In addition, we obtain Lorentz-Sobolev estimates for solutions to the obstacle problem and others applications.