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

共 50 条

[21] ON THE CONVEXITY OF A SOLUTION OF LIOUVILLE EQUATION
GUSTAFSSON, B
DUKE MATHEMATICAL JOURNAL, 1990, 60 (02) : 303 - 311
[22] Stochastic Loewner evolution in doubly connected domains
Dapeng Zhan
Probability Theory and Related Fields, 2004, 129 : 340 - 380
[23] Universal Taylor Series on Doubly Connected Domains
Athanassia G. Bacharoglou
Results in Mathematics, 2009, 53 : 9 - 18
[24] Doubly connected wandering domains for meromorphic functions
Dominguez, Patricia
Sienra, Guillermo
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2010, 55 (04) : 407 - 416
[25] The theory of conformed representation in doubly connected domains
Khajalia, GJ
COMPTES RENDUS DE L ACADEMIE DES SCIENCES DE L URSS, 1940, 26 : 550 - 551
[26] VARIATIONAL SOLUTION OF A LIOUVILLE EQUATION
ANDERSON, N
ARTHURS, AM
LETTERE AL NUOVO CIMENTO, 1971, 2 (09): : 481 - &
[27] Boundary value problems for a mixed-type equation in domains with a doubly connected hyperbolicity subdomain
M. E. Lerner
O. A. Repin
Differential Equations, 2000, 36 : 1502 - 1506
[28] Boundary value problems for a mixed-type equation in domains with a doubly connected hyperbolicity subdomain
Lerner, ME
Repin, OA
DIFFERENTIAL EQUATIONS, 2000, 36 (10) : 1502 - 1506
[29] AN INTEGRAL-EQUATION METHOD FOR THE NUMERICAL CONFORMAL MAPPING OF INTERIOR, EXTERIOR AND DOUBLY-CONNECTED DOMAINS
HOUGH, DM
PAPAMICHAEL, N
NUMERISCHE MATHEMATIK, 1983, 41 (03) : 287 - 307
[30] Cauchy Problem for the Laplace Equation in 2D and 3D Doubly Connected Domains
Liu, Ji-Chuan
Zhang, Quan-Guo
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2013, 93 (03): : 203 - 219

← 1 2 3 4 5 →