ASYMPTOTIC BEHAVIOR OF BLOWUP SOLUTIONS FOR ELLIPTIC EQUATIONS WITH EXPONENTIAL NONLINEARITY AND SINGULAR DATA

被引：31
作者：
Zhang, Lei [1 ]
机构：
[1] Univ Alabama, Dept Math, Birmingham, AL 35294 USA
来源：
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2009年 / 11卷 / 03期
基金：
美国国家科学基金会;
关键词：
Liouville equation; blowup analysis; MEAN-FIELD EQUATIONS; TODA SYSTEM; MULTIVORTEX SOLUTIONS; TOPOLOGICAL-DEGREE; ELECTROWEAK THEORY; RIEMANN SURFACES; ANALYTIC ASPECTS; UP SOLUTIONS; EXISTENCE; SYMMETRY;
D O I：
10.1142/S0219199709003417
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a sequence of blowup solutions of a two-dimensional, second-order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of Bartolucci-Chen-Lin-Tarantello, it is proved that the pro. le of the solutions differs from global solutions of a Liouville-type equation only by a uniformly bounded term. The present paper improves their result and establishes an expansion of the solutions near the blowup points with a sharp error estimate.
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收藏
页码：395 / 411
页数：17
相关论文
共 36 条
[1]   A MAGNETIC CONDENSATE SOLUTION OF THE CLASSICAL ELECTROWEAK THEORY [J].
AMBJORN, J ;
OLESEN, P .
PHYSICS LETTERS B, 1989, 218 (01) :67-71
[2]   Profile of blow-up solutions to Mean Field equations with singular data [J].
Bartolucci, D ;
Chen, CC ;
Lin, CS ;
Tarantello, G .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2004, 29 (7-8) :1241-1265
[3]   Liouville type equations with singular data and their applications to periodic multivortices for the Electroweak Theory [J].
Bartolucci, D ;
Thrantello, G .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2002, 229 (01) :3-47
[4]   A SUP PLUS INF INEQUALITY FOR SOME NONLINEAR ELLIPTIC-EQUATIONS INVOLVING EXPONENTIAL NONLINEARITIES [J].
BREZIS, H ;
LI, YY ;
SHAFRIR, I .
JOURNAL OF FUNCTIONAL ANALYSIS, 1993, 115 (02) :344-358
[5]   UNIFORM ESTIMATES AND BLOW UP BEHAVIOR FOR SOLUTIONS OF -DELTA-U = V(X)EU IN 2 DIMENSIONS [J].
BREZIS, H ;
MERLE, F .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1991, 16 (8-9) :1223-1253
[6]   VORTEX CONDENSATION IN THE CHERN-SIMONS HIGGS-MODEL - AN EXISTENCE THEOREM [J].
CAFFARELLI, LA ;
YANG, YS .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1995, 168 (02) :321-336
[7]   The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory [J].
Chae, D ;
Imanuvilov, OY .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2000, 215 (01) :119-142
[8]  
Chang S-YA., 2003, NEW STUD ADV MATH, P61
[9]  
Chanillo S, 2000, DUKE MATH J, V105, P309
[10]   Sharp estimates for solutions of multi-bubbles in compact Riemann surfaces [J].
Chen, CC ;
Lin, CS .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2002, 55 (06) :728-771
1234