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

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.