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

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 $\mathrm{\Omega }$ and $\beta \cdot Du+\gamma u=g$ on $\mathrm{\partial }\mathrm{\Omega }$, where $\mathrm{\Omega }$ is a bounded domain in ${\mathbb{R}}^n$ ($n\ge 2$), 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.