遍历均值场博弈：索博列夫临界情况下局部最小值的存在性

IF 2.1 2区数学 Q1 MATHEMATICS

Calculus of Variations and Partial Differential Equations Pub Date : 2024-05-13 DOI:10.1007/s00526-024-02744-2

Marco Cirant, Alessandro Cosenza, Gianmaria Verzini

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引用次数: 0

摘要

我们研究了粘性遍历均场博弈系统在有界域中的解的存在性，该有界域具有诺伊曼边界条件和局部可能的聚集耦合。特别是，我们利用相关的变分结构，寻找合适函数的约束最小值。根据耦合的增长情况，我们发现在质量次临界和临界情况下存在全局最小值，在质量超临界情况下存在局部最小值，特别是在索博列夫临界情况下。

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Ergodic mean field games: existence of local minimizers up to the Sobolev critical case

We investigate the existence of solutions to viscous ergodic Mean Field Games systems in bounded domains with Neumann boundary conditions and local, possibly aggregative couplings. In particular we exploit the associated variational structure and search for constrained minimizers of a suitable functional. Depending on the growth of the coupling, we detect the existence of global minimizers in the mass subcritical and critical case, and of local minimizers in the mass supercritical case, notably up to the Sobolev critical case.

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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.