Profile of Blow-up Solutions to Mean Field Equations with Singular Data
Profile of Blow-up Solutions to Mean Field Equations with Singular Data
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DOI：
10.1081/pde-200033739
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发表时间：
2004-01
影响因子：
1.9
通讯作者：
D. Bartolucci;Chiun-Chuan Chen;Changshou Lin;G. Tarantello
中科院分区：
文献类型：
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作者：
D. Bartolucci;Chiun-Chuan Chen;Changshou Lin;G. Tarantello
摘要受规范场论中自对偶涡旋研究的启发，我们考虑了紧致曲面上一类Liouville型平均场方程，该方程包含由Dirac测度指定的奇异数据，且这些奇异数据支持在多个点（所谓的涡旋点）上。根据应用的需要，我们需要描述精确集中在给定涡点的解序列的爆破行为。我们提供了准确的逐点估计的泡沫序列的配置文件，以及“sup + inf”估计的解决方案。这些结果推广了Li [Li，Y. Y.（1999年）。Harnack型不等式：移动平面的方法。200：421-444]和Brezis等人[Brezis，H.，Li，Y.沙夫里尔岛（1993年）。一类含指数项的非线性椭圆型方程的一个sup + inf不等式。J. Funct. Anal. 115：344-358]相对于“经常”的情况下，即在缺乏单一来源。
Abstract Motivated by the study of selfdual vortices in gauge field theory, we consider a class of Mean Field equations of Liouville-type on compact surfaces involving singular data assigned by Dirac measures supported at finitely many points (the so called vortex points). According to the applications, we need to describe the blow-up behavior of solution-sequences which concentrate exactly at the given vortex points. We provide accurate pointwise estimates for the profile of the bubbling sequences as well as “sup + inf” estimates for solutions. Those results extend previous work of Li [Li, Y. Y. (1999). Harnack type inequality: The method of moving planes. Comm. Math. Phys. 200:421–444] and Brezis et al. [Brezis, H., Li, Y. Shafrir, I. (1993). A sup + inf inequality for some nonlinear elliptic equations involving the exponential nonlinearities. J. Funct. Anal. 115: 344–358] relative to the “regular” case, namely in absence of singular sources.