Sobolev regularity for first order mean field games
| Autor: | Alpár Richárd Mészáros, P. Jameson Graber |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Applied Mathematics
010102 general mathematics Mathematics::Analysis of PDEs Coercivity Coupling (probability) 01 natural sciences 010101 applied mathematics Sobolev space Mean field theory Bellman equation Applied mathematics Order (group theory) 0101 mathematics Mathematical Physics Analysis Hamiltonian (control theory) Mathematics Variable (mathematics) |
| Zdroj: | Annales de l'Institut Henri Poincaré C, analyse non linéaire, 2018, Vol.35(6), pp.1557-1576 [Peer Reviewed Journal] |
| DOI: | 10.1016/j.anihpc.2018.01.002 |
| Popis: | In this paper we obtain Sobolev estimates for weak solutions of first order variational Mean Field Game systems with coupling terms that are local functions of the density variable. Under some coercivity conditions on the coupling, we obtain first order Sobolev estimates for the density variable, while under similar coercivity conditions on the Hamiltonian we obtain second order Sobolev estimates for the value function. These results are valid both for stationary and time-dependent problems. In the latter case the estimates are fully global in time, thus we resolve a question which was left open in [23] . Our methods apply to a large class of Hamiltonians and coupling functions. |
| Databáze: | OpenAIRE |
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