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

TL;DR

This paper investigates a nonlinear elliptic equation in an unbounded sector, establishing the existence of minimal solutions, analyzing their properties, and applying these results to plasma physics stationary solutions.

Contribution

It introduces new existence and property results for solutions of a nonlinear elliptic PDE in unbounded sectors, with applications to plasma equilibrium models.

Findings

Existence of minimal solutions in unbounded sectors.

Asymptotic behavior of solutions related to plasma physics.

Application of mathematical analysis to physical plasma models.

Abstract

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.