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

preprint2014arXivOpen access

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.

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

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The Dirichlet problem for −Δφ=e−φ-Δφ= \mathrm{e}^{-φ}−Δφ=e−φ in an infinite sector. Application to plasma equilibria

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