  In this article we are interested in studying regularity up to the boundary
for one-phase singularly perturbed fully nonlinear elliptic problems,
associated to high energy activation potentials, namely $$
  F(X, \nabla u^{\varepsilon}, D^2 u^{\varepsilon}) =
\zeta_{\varepsilon}(u^{\varepsilon})
  \quad \mbox{in} \quad \Omega \subset \R^n $$ where $\zeta_{\varepsilon}$
behaves asymptotically as the Dirac measure $\delta_{0}$ as $\varepsilon$ goes
to zero. We shall establish global gradient bounds independent of the parameter
$\varepsilon$.
