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

We derive global W2,p estimates (with n < p < degrees degrees) for viscosity solutions to fully nonlinear elliptic equations under relaxed structural assumptions on the governing operator that are weaker than convexity and oblique boundary conditions as follows: for f e Lp(O) and under appropriate assumptions on the data ss, gamma, g and S2 c Rn. Our approach makes use of geometric tangential methods, which consist of importing "fine regularity estimates" from a limiting pro -file, i.e., the Recession operator, associated with the original second-order one via compactness and stability procedures. As a result, we pay special attention to the borderline scenario, i.e., f e BMOp 2 L degrees degrees. In such a setting, we prove that solutions enjoy BMOp type estimates for their second derivatives. Finally, as another application of our findings, we obtain Hessian estimates to obstacle-type problems under oblique boundary conditions and no convexity assumptions, which may have their own mathematical interest. A density result for a suitable class of viscosity solutions will also be addressed. (c) 2023 Elsevier Inc. All rights reserved.