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In this work we derive global estimates for viscosity solutions to fullynonlinear elliptic equations under relaxed structural assumptions on thegoverning operator which are weaker than convexity and oblique boundaryconditions and under suitable assumptions on the dat. Our approach makes use ofgeometric tangential methods, which consists of importing "fine regularityestimates" from a limiting profile, i.e., the Recession operator, associatedwith the original second order one via compactness and stability procedures. Asa result, we devote a special attention to the borderline scenario. In such asetting, we prove that solutions enjoy BMO type estimates for their secondderivatives. In the end, as another application of our findings, we obtainHessian estimates to obstacle type problems under oblique boundary conditionsand no convexity assumptions, which may have their own mathematical interest. Adensity result in a suitable class of viscosity solutions will be alsoaddressed.

Sharp Hessian estimates for fully nonlinear elliptic equations under relaxed convexity assumptions, oblique boundary conditions and applications