In this paper we consider the Liouville equation Δu+λ2eu=0 with Dirichlet boundary conditions in a two dimensional, doubly connected domain Ω. We show that there exists a simple, closed curve γ⊂Ω such that for a sequence λn→0 and a sequence of solutions un it holds [Formula presented], where H is a harmonic function in Ω∖γ and [Formula presented], where cΩ is a constant depending on the conformal class of Ω only.
Maximal solution of the Liouville equation in doubly connected domains
Vaira G.
2019-01-01
Abstract
In this paper we consider the Liouville equation Δu+λ2eu=0 with Dirichlet boundary conditions in a two dimensional, doubly connected domain Ω. We show that there exists a simple, closed curve γ⊂Ω such that for a sequence λn→0 and a sequence of solutions un it holds [Formula presented], where H is a harmonic function in Ω∖γ and [Formula presented], where cΩ is a constant depending on the conformal class of Ω only.File in questo prodotto:
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