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: \(\left\{ \begin{array}{rclcl} F(D^2u,Du,u,x) & =& f(x)& \text {in} & \Omega \\ \beta \cdot Du + \gamma u& =& g & \text {on}& \partial \Omega ,\end{array}\right. \) $$\left\{\begin{array}{ccccc}\hfill F(D^{2}u,Du,u,x)& =& f(x)\hfill & \text{in}& \mathrm{\Omega }\hfill \\ \hfill \beta ·Du+\gamma u& =& g\hfill & \text{on}& \partial \mathrm{\Omega },\hfill \end{array}\right)$$ where \(\Omega \) $\mathrm{\Omega }$ is a bounded domain in \(\mathbb {R}^{n}\) ${\mathbb{R}}^n$ ( \(n\ge 2\) $n\ge 2$ ), under suitable assumptions on the source term f, data \(\beta , \gamma \) $\beta ,\gamma$ and g. In addition, we obtain Lorentz-Sobolev estimates for solutions to the obstacle problem and others applications.