caa a22 4500 60551495X CHVBK 20210128100707.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s00205-014-0799-9 doi (NATIONALLICENCE)springer-10.1007/s00205-014-0799-9 Porretta Alessio Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133, Roma, Italy aut Weak Solutions to Fokker-Planck Equations and Mean Field Games [Elektronische Daten] [Alessio Porretta] We deal with systems of PDEs, arising in mean field games theory, where viscous Hamilton-Jacobi and Fokker-Planck equations are coupled in a forward-backward structure. We consider the case of local coupling, when the running cost depends on the pointwise value of the distribution density of the agents, in which case the smoothness of solutions is mostly unknown. We develop a complete weak theory, proving that those systems are well-posed in the class of weak solutions for monotone couplings under general growth conditions, and for superlinear convex Hamiltonians. As a key tool, we prove new results for Fokker-Planck equations under minimal assumptions on the drift, through a characterization of weak and renormalized solutions. The results obtained give new perspectives even for the case of uncoupled equations as far as the uniqueness of weak solutions is concerned. Springer-Verlag Berlin Heidelberg, 2014 Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/1(2015-04-01), 1-62 0003-9527 216:1<1 2015 216 205 https://doi.org/10.1007/s00205-014-0799-9 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/s00205-014-0799-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Porretta Alessio Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133, Roma, Italy aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/1(2015-04-01), 1-62 0003-9527 216:1<1 2015 216 205