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 $\hat{I}\text{c◯}$ and ${\hat{I}}^2\cdot Du+{\hat{I}}^{3}u=g$ on $\partial \hat{I}\text{c◯}$, where $\hat{I}\text{c◯}$ is a bounded domain in ${\mathbb{R}}^n$ ($n\ge 2$), under suitable assumptions on the source term f, data ${\hat{I}}^2$, ${\hat{I}}^3$ and g. In addition, we obtain Lorentz-Sobolev estimates for solutions to the obstacle problem and others applications.

25 pages