caa a22 4500 60619438X CHVBK 20210128100914.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00030-015-0323-4 doi (NATIONALLICENCE)springer-10.1007/s00030-015-0323-4 Second order mean field games with degenerate diffusion and local coupling [Elektronische Daten] [Pierre Cardaliaguet, P. Graber, Alessio Porretta, Daniela Tonon] We analyze a (possibly degenerate) second order mean field games system of partial differential equations. The distinguishing features of the model considered are (1) that it is not uniformly parabolic, including the first order case as a possibility, and (2) the coupling is a local operator on the density. As a result we look for weak, not smooth, solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as minimizers of two optimal control problems. We also show that such solutions are stable with respect to the data, so that in particular the degenerate case can be approximated by a uniformly parabolic (viscous) perturbation. Springer Basel, 2015 Cardaliaguet Pierre Ceremade, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris cedex 16, France aut Graber P. 828, Boulevard des Maréchaux, 91762, Palaiseau Cedex, France aut Porretta Alessio Dipartimento di Matematica, Università di Roma "Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Roma, Italy aut Tonon Daniela Ceremade, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris cedex 16, France aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/5(2015-10-01), 1287-1317 1021-9722 22:5<1287 2015 22 30 https://doi.org/10.1007/s00030-015-0323-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-015-0323-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cardaliaguet Pierre Ceremade, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris cedex 16, France aut NATIONALLICENCE 700 1- Graber P. 828, Boulevard des Maréchaux, 91762, Palaiseau Cedex, France aut NATIONALLICENCE 700 1- Porretta Alessio Dipartimento di Matematica, Università di Roma "Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Roma, Italy aut NATIONALLICENCE 700 1- Tonon Daniela Ceremade, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris cedex 16, France aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/5(2015-10-01), 1287-1317 1021-9722 22:5<1287 2015 22 30