Semi-linear parabolic equations on homogenous Lie groups arising from mean field games
P Mannucci, C Marchi, C Mendico - Mathematische Annalen, 2024 - Springer
P Mannucci, C Marchi, C Mendico
Mathematische Annalen, 2024•SpringerThe 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 …
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 …
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.
Springer
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