广义塞伯格-维滕函数的变量问题

IF 2.1 2区数学 Q1 MATHEMATICS

Calculus of Variations and Partial Differential Equations Pub Date : 2024-07-16 DOI:10.1007/s00526-024-02771-z

Wanjun Ai, Shuhan Jiang, Jürgen Jost

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引用次数: 0

摘要

在本文中，作为对量子场论中的规整函数进行统一数学处理的一步，我们对塞伯格-维滕函数进行了广义化，尤其是将卡普斯坦-维滕函数作为一个特例。我们首先证明了这个广义函数弱解的平滑性。然后，我们通过验证 Palais-Smale compactness（帕莱斯-斯马尔紧凑性），确定了在束的结构群是无性的假设下弱解的存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Variational aspects of the generalized Seiberg–Witten functional

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Variational aspects of the generalized Seiberg–Witten functional

In this paper, as a step towards a unified mathematical treatment of the gauge functionals from quantum field theory that have found profound applications in mathematics, we generalize the Seiberg–Witten functional that in particular includes the Kapustin–Witten functional as a special case. We first demonstrate the smoothness of weak solutions to this generalized functional. We then establish the existence of weak solutions under the assumption that the structure group of the bundle is abelian, by verifying the Palais–Smale compactness.

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来源期刊

Calculus of Variations and Partial Differential Equations 数学-数学

CiteScore

3.30

自引率

4.80%

发文量

224

审稿时长

6 months

期刊介绍： Calculus of variations and partial differential equations are classical, very active, closely related areas of mathematics, with important ramifications in differential geometry and mathematical physics. In the last four decades this subject has enjoyed a flourishing development worldwide, which is still continuing and extending to broader perspectives. This journal will attract and collect many of the important top-quality contributions to this field of research, and stress the interactions between analysts, geometers, and physicists. The field of Calculus of Variations and Partial Differential Equations is extensive; nonetheless, the journal will be open to all interesting new developments. Topics to be covered include: - Minimization problems for variational integrals, existence and regularity theory for minimizers and critical points, geometric measure theory - Variational methods for partial differential equations, optimal mass transportation, linear and nonlinear eigenvalue problems - Variational problems in differential and complex geometry - Variational methods in global analysis and topology - Dynamical systems, symplectic geometry, periodic solutions of Hamiltonian systems - Variational methods in mathematical physics, nonlinear elasticity, asymptotic variational problems, homogenization, capillarity phenomena, free boundary problems and phase transitions - Monge-Ampère equations and other fully nonlinear partial differential equations related to problems in differential geometry, complex geometry, and physics.