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arXiv · 1805.01147

A note on non-coercive first order Mean Field Games with analytic data

Paola Mannucci·Claudio Marchi·Carlo Mariconda·Nicoletta Tchou
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Abstract

We study first order evolutive Mean Field Games whose operators are non-coercive. This situation occurs, for instance, when some directions are `forbidden' to the generic player at some points. Under some regularity assumptions, we establish existence of a weak solution of the system. Mainly, we shall describe the evolution of the population's distribution as the push-forward of the initial distribution through a flow, suitably defined in terms of the underlying optimal control problem.

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Paola Mannucci, Claudio Marchi, Carlo Mariconda, Nicoletta Tchou. 2018-05-03. A note on non-coercive first order Mean Field Games with analytic data. https://arxiv.org/abs/1805.01147

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