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

Abstract

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

where ${\zeta }_{\epsilon }$ behaves asymptotically as the Dirac measure ${\delta }_0$ as $\epsilon$ goes to zero. We shall establish global gradient bounds independent of the parameter $\epsilon$.