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 EDP - Equations aux dérivées partielles

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: Nonlinear elliptic equations; unbounded domains; plasma physics

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.. 2014. ⟨hal-01009131v1⟩