Global Lorentz-type regularity for non-convex fully nonlinear elliptic equations with oblique boundary conditions and applications

We establish new global regularity estimates for the Hessian of viscosity solutions to non-convex fully nonlinear elliptic equations with oblique boundary conditions in the setting of weighted Lorentz and Morrey-Lorentz spaces. More precisely, our approach relies on an analysis of the ellipticity coefficients of the governing operator and, under suitable small-aperture assumptions, we obtain Calderón-Zygmund type estimates in weighted Lorentz spaces. As a byproduct of this result, we derive several applications, including Sobolev estimates with variable exponents and the study of the obstacle problem with an oblique boundary condition.