Maximal solution of the Liouville equation in doubly connected domains

被引：3

作者：

Kowalczyk, Michal ^{[1
,2
]}

Pistoia, Angela ^{[3
]}

Vaira, Giusi ^{[4
]}

机构：

[1] Univ Chile, Dept Ingn Matemat, Casilla 170 Correo 3, Santiago, Chile

[2] Univ Chile, Ctr Modelamiento Matemat, UMI 2807, CNRS, Casilla 170 Correo 3, Santiago, Chile

[3] Sapienza Univ Roma, Dipartimento SBAI, Via Antonio Scarpa 16, I-00161 Rome, Italy

[4] Univ Campania L Vanvitelli, Dipartimento Matemat & Fis, Viale Lincoln 5, I-81100 Caserta, Italy

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2019年 / 277卷 / 09期

关键词：

Lionville equation; Minimal solution; Bubbling solutions; Maximal solution; 2-DIMENSIONAL EULER EQUATIONS; BLOW-UP ANALYSIS; STATISTICAL-MECHANICS; MULTIVORTEX SOLUTIONS; STATIONARY FLOWS; RADIAL SOLUTIONS; SINGULAR LIMITS; UNBOUNDED MASS; STEADY-STATES; EXISTENCE;

D O I：

10.1016/j.jfa.2019.06.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider the Liouville equation Delta u+lambda(2)e(u) = 0 with Dirichlet boundary conditions in a two dimensional, doubly connected domain Omega. We show that there exists a simple, closed curve gamma subset of Omega such that for a sequence lambda(n) -> 0 and a sequence of solutions u(n) it holds u(n)/log 1/lambda(n) -> H, where H is a harmonic function in Omega\gamma and lambda(2)(n)/log 1/lambda(n) integral(Omega)e(un) dx -> 8 pi c(Omega), where c(Omega) is a constant depending on the conformal class of Omega only. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：2997 / 3050

页数：54

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