Regularity up to the boundary for singularly perturbed fully nonlinear elliptic equations

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 $$ F(X, nabla u^{varepsilon}, D^2 u^{varepsilon}) = zeta_{varepsilon}(u^{varepsilon}) mbox{in} quad Omega subset R^n $$ 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 $varepsilon$.