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Title

Semi-linear parabolic equations on homogenous Lie groups arising from mean field games.

Authors

Mannucci, Paola; Marchi, Claudio; Mendico, Cristian

Abstract

The existence and the uniqueness of solutions to some semilinear parabolic equations on homogeneous Lie groups, namely, the Fokker–Planck equation and the Hamilton–Jacobi equation, are addressed. The anisotropic geometry of the state space plays a crucial role in our analysis and creates several issues that need to be overcome. Indeed, the ellipticity directions span, at any point, subspaces of dimension strictly less than the dimension of the state space. Finally, the above results are used to obtain the short-time existence of classical solutions to the mean field games system defined on an homogenous Lie group.

Subjects

EQUATIONS; GEOMETRY; FOKKER-Planck equation; HAMILTON-Jacobi equations; GAMES; LIE groups

Publication

Mathematische Annalen, 2024, Vol 390, Issue 2, p3077

ISSN

0025-5831

Publication type

Academic Journal

DOI

10.1007/s00208-024-02819-7

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