Sharp semi-concavity in a non-autonomous control problem and Lp estimates in an optimal-exit MFG

• Published in: Nonlinear differential equations and applications Vol. 27; no. 2
• Main Authors: Dweik, Samer, Mazanti, Guilherme
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 2020; Springer Nature B.V
• Subjects: Analysis; Concavity; Game theory; Mathematics; Mathematics and Statistics; Optimal control; Regularity; Travel time; 91A13; MFG system; 49N70; Semi-concavity of the value function; 93C15; estimate; 35B65; Mean field games; Non-autonomous optimal control; 49J15

This paper studies a mean field game inspired by crowd motion in which agents evolve in a compact domain and want to reach its boundary minimizing the sum of their travel time and a given boundary cost. Interactions between agents occur through their dynamic, which depends on the distribution of all...