The Dirichlet problem for $-\Delta \varphi= \mathrm{e}^{-\varphi}$ in an infinite sector. Application to plasma equilibria
Analysis of PDEs
2014-09-01 v1
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.
Cite
@article{arxiv.1408.6945,
title = {The Dirichlet problem for $-\Delta \varphi= \mathrm{e}^{-\varphi}$ in an infinite sector. Application to plasma equilibria},
author = {Olivier Goubet and Simon Labrunie},
journal= {arXiv preprint arXiv:1408.6945},
year = {2014}
}