Convergence for a Liouville equation | Zendy

Li Ma | Zendy; Juncheng Wei | Zendy

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Convergence for a Liouville equation

Author(s) -

Li Ma,

Juncheng Wei

Publication year - 2001

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/pl00013216

Subject(s) - mathematics , bounded function , convergence (economics) , domain (mathematical analysis) , sequence (biology) , mathematical analysis , liouville equation , statistical mechanics , plane (geometry) , dirichlet problem , dirichlet boundary condition , bubble , boundary value problem , geometry , statistical physics , physics , quantum mechanics , biology , economics , quantum , genetics , economic growth , parallel computing , computer science

. In this paper, we study the asymptotic behavior of solutions of the Dirichlet problem for the Liouville equation ¶¶¶¶on a bounded smooth domain in the plane as , where . The equation is also called the Mean Field Equation in Statistical Mechanics. By a result of H. Brezis and F. Merle, any solution sequence may have a finite number of bubbles. We give a necessary condition for the location of the bubble points.

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