JournalsifbVol. 17, No. 3pp. 317–332

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

  • Gleydson C. Ricarte

    Universidade Federal do Ceará, Fortaleza, Brazil
  • João Vítor da Silva

    Universidade Federal do Ceará, Fortaleza, Brazil
Regularity up to the boundary for singularly perturbed fully nonlinear elliptic equations cover

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

F(X,uε,D2uε)=ζϵ(uϵ)\mboxinΩRnF(X, \nabla u^{\varepsilon}, D^2 u^{\varepsilon}) = \zeta_{\epsilon}(u^{\epsilon}) \quad \mbox{in} \quad \Omega \subset \mathbb R^n

where ζε\zeta_{\varepsilon} behaves asymptotically as the Dirac measure δ0\delta_{0} as ε\varepsilon goes to zero. We shall establish global gradient bounds independent of the parameter ε\varepsilon.

Cite this article

Gleydson C. Ricarte, João Vítor da Silva, Regularity up to the boundary for singularly perturbed fully nonlinear elliptic equations. Interfaces Free Bound. 17 (2015), no. 3, pp. 317–332

DOI 10.4171/IFB/344