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

$$
F(X, \nabla u^{\varepsilon}, D^2 u^{\varepsilon}) = \zeta_{\epsilon}(u^{\epsilon}) \quad \text{in} \quad \Omega \subset \mathbb R^n
$$

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 $\varepsilon$.

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

Gleydson C. Ricarte

João Vítor da Silva

Abstract

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