On the Boundary Ergodic Problem for Fully Nonlinear Equations in Bounded Domains with General Nonlinear Neumann Boundary Conditions

Guy Barles (1) , Francesca da Lio (2)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 Dipartimento di Matematica "Giuseppe Peano" [Torino]

We study nonlinear Neumann type boundary value problems related to ergodic phenomenas. The particularity of these problems is that the ergodic constant appears in the (possibly nonlinear) Neumann boundary conditions. We provide, for bounded domains, several results on the existence, uniqueness and properties of this ergodic constant.

Mots clés: boundary ergodic problem; Neumann boundary conditions; fully nonlinear equations; viscosity solutions

Domaines: Equations aux dérivées partielles [math.AP]

Guy Barles, Francesca da Lio. On the Boundary Ergodic Problem for Fully Nonlinear Equations in Bounded Domains with General Nonlinear Neumann Boundary Conditions. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2005, 22 (5), pp.521--541. ⟨hal-00002826⟩