  We consider a function U satisfying a degenerate elliptic equation on
(0,+\infty)\times R^N with mixed Dirichlet-Neumann boundary conditions. The
Neumann condition is prescribed on a bounded domain \Omega\subset R^N of class
C^{1;1}, whereas the Dirichlet data is on the exterior of \Omega. We prove
Holder regularity estimates of U/d^s, where d is a distance function defined
as d(z) := dist(z;R^N\setminus\Omega), for z\in (0,+\infty)\times R^N. The
degenerate elliptic equation arises from the Caffarelli-Silvestre extension of
the Dirichlet problem for the fractional Laplacian. Our proof relies on
compactness and blow-up analysis arguments.
