The Dirichlet problem for $-\Delta \varphi= \mathrm{e}^{-\varphi}$ in an infinite sector. Application to plasma equilibria.

Olivier Goubet (1) , Simon Labrunie (2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
2 IECL - Institut Élie Cartan de Lorraine

We consider here a nonlinear elliptic equation in an unbounded sectorial domain of the plane. We prove the existence of a minimal solution to this equation and study its properties. We infer from this analysis some asymptotics for the stationary solution of an equation arising in plasma physics.

Mots clés: unbounded domains; plasma physics; Nonlinear elliptic equations

Domaines: Equations aux dérivées partielles [math.AP]

Olivier Goubet, Simon Labrunie. The Dirichlet problem for $-\Delta \varphi= \mathrm{e}^{-\varphi}$ in an infinite sector. Application to plasma equilibria.. Nonlinear Analysis: Theory, Methods and Applications, 2015, 119, pp.115-126. ⟨10.1016/j.na.2014.08.015⟩. ⟨hal-01009131v2⟩