Nonsmooth mean field games with state constraints

In this paper, we consider a mean field game model inspired by crowd motion where agents aim to reach closed set, called target in minimal time. Congestion phenomena are modeled through constraint on the velocity of an agent that depends average density around their position. The is considered presence state constraints: roughly speaking, these constraints may walls, columns, fences, hedges, or other kinds obstacles at boundary domain which cannot cross. After providing more detailed description model, paper recalls some previous results existence equilibria for such games and presents main difficulties arise due constraints. Our contribution show satisfy system coupled partial differential equations, known system, thanks recent techniques characterize optimal controls These not only allow deal with but also require very few regularity assumptions dynamics agents.