Details

Autor(en) / Beteiligte

• Ricarte, Gleydson
• da Silva, João Vítor

Titel

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

Ist Teil von

• Interfaces and free boundaries, 2015-01, Vol.17 (3), p.317-332

Ort / Verlag

Zuerich, Switzerland: European Mathematical Society Publishing House

Erscheinungsjahr

2015

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

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