具有Neumann条件的有界域上的主方程

IF 2.1 2区数学 Q1 MATHEMATICS

Communications in Partial Differential Equations Pub Date : 2021-05-18 DOI:10.1080/03605302.2021.2008965

M. Ricciardi

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引用次数: 6

摘要

摘要本文在Neumann边界条件的框架下研究了平均场对策主方程的适定性。解的定义与平均场对策系统的经典定义密切相关，但这里的边界条件导致了主方程公式中的两个Neumann条件，即空间和测度。通过深入研究一类合适的抛物型方程的边界条件和边界上的全局正则性，得到了线性化系统的全局正则化，这对于证明解的存在性至关重要。

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The Master Equation in a bounded domain with Neumann conditions

Abstract In this article, we study the well-posedness of the Master Equation of Mean Field Games in a framework of Neumann boundary condition. The definition of solution is closely related to the classical one of the Mean Field Games system, but the boundary condition here leads to two Neumann conditions in the Master Equation formulation, for both space and measure. The global regularity of the linearized system, which is crucial in order to prove the existence of solutions, is obtained with a deep study of the boundary conditions and the global regularity at the boundary of a suitable class of parabolic equations.

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来源期刊

Communications in Partial Differential Equations 数学-数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal aims to publish high quality papers concerning any theoretical aspect of partial differential equations, as well as its applications to other areas of mathematics. Suitability of any paper is at the discretion of the editors. We seek to present the most significant advances in this central field to a wide readership which includes researchers and graduate students in mathematics and the more mathematical aspects of physics and engineering.