  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 H\"older estimate for
solutions, obtained by means of the comparison principle and the construction
of ad hoc barriers. The global H\"older 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.

Analysis of PDEs