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 / Kowalczyk, M.; Pistoia, A.; Vaira, G.. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 277:9(2019), pp. 2997-3050. [10.1016/j.jfa.2019.06.013]
Maximal solution of the Liouville equation in doubly connected domains
Pistoia A.;
2019
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 | Dimensione | Formato | |
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