Mean Field Equation of Liouville Type with Singular Data: Topological Degree

被引：71

作者：

Chen, Chiun-Chuan ^{[1
]}

Lin, Chang-Shou ^{[2
]}

机构：

[1] Natl Taiwan Univ, Natl Ctr Theoret Sci, Taipei 10617, Taiwan

[2] Natl Taiwan Univ, Taida Inst Math Sci, Ctr Adv Study Theoret Sci, Taipei 10617, Taiwan

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2015年 / 68卷 / 06期

关键词：

BLOW-UP SOLUTIONS; 2-DIMENSIONAL EULER EQUATIONS; STATISTICAL-MECHANICS; ELECTROWEAK THEORY; CONDENSATE SOLUTION; CONFORMAL METRICS; STATIONARY FLOWS; EXISTENCE; INEQUALITY; CURVATURE;

D O I：

10.1002/cpa.21532

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the following mean field equation: (qj-1)onM, where M is a compact Riemann surface with volume 1, h* is a positive C-1 function on M, and and (j) are constants satisfying (j)>-1. In this paper, we derive the topological-degree-counting formula for noncritical values of . We also give several applications of this formula, including existence of the curvature +1 metric with conic singularities, doubly periodic solutions of electroweak theory, and a special case of self-gravitating strings. (c) 2015 Wiley Periodicals, Inc.

引用

页码：887 / 947

页数：61

共 58 条

[31] SELF-DUAL CHERN-SIMONS VORTICES [J].

JACKIW, R ;

WEINBERG, EJ .

PHYSICAL REVIEW LETTERS, 1990, 64 (19) :2234-2237

[32] Analytic aspects of the Toda system II: Bubbling behavior and existence of solutions [J].

Jost, J ;

Lin, CS ;

Wang, GF .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2006, 59 (04) :526-558

[33] STATISTICAL-MECHANICS OF CLASSICAL PARTICLES WITH LOGARITHMIC INTERACTIONS [J].

KIESSLING, MKH .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1993, 46 (01) :27-56

[34] Harnack type inequality: the method of moving planes [J].

Li, YY .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1999, 200 (02) :421-444

[35] BLOW-UP ANALYSIS FOR SOLUTIONS OF -DELTA-U=VE(U) IN DIMENSION-2 [J].

LI, YY ;

SHAFRIR, I .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1994, 43 (04) :1255-1270

[36] Existence of Bubbling Solutions for Chern-Simons Model on a Torus [J].

Lin, Chang-Shou ;

Yan, Shusen .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2013, 207 (02) :353-392

[37]

Lin CS, 2010, ANN MATH, V172, P911

[38] Bubbling Solutions for Relativistic Abelian Chern-Simons Model on a Torus [J].

Lin, Chang-Shou ;

Yan, Shusen .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2010, 297 (03) :733-758

[39] Topological degree for mean field equations on S2 [J].

Lin, CS .

DUKE MATHEMATICAL JOURNAL, 2000, 104 (03) :501-536

[40]

Lin CS, 2000, CALC VAR PARTIAL DIF, V10, P291, DOI 10.1007/s005269900026

← 1 2 3 4 5 6 →