Mixed boundary value problems for fully nonlinear degenerate or singular equations. (October 2022) - Birindelli, Isabeau; Demengel, Françoise; Leoni, Fabiana
Abstract: We prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global Hölder estimate for solutions, obtained by means of the comparison principle and the construction of ad hoc barriers. The global Hölder estimate immediately yields a compactness result in the space of solutions, which could be applied in the study of principal eigenvalues and principal eigenfunctions of mixed boundary value problems.