On stationary fractional mean field games

Journal des Mathematiques Pures et Appliquees

Volumn 122, Issue , 2019, Pages 1-22

  Cesaroni, Annalisa ^a   Cirant, Marco ^a   Dipierro, Serena ^b   Novaga, Matteo ^c   Valdinoci, Enrico ^b,d,e  

^a UNIVERSITY OF PADOVA   (Italy)

^b UNIVERSITY OF MILAN   (Italy)

^c UNIVERSITY OF PISA   (Italy)

^d UNIVERSITY OF MELBOURNE   (Australia)

^e CNR   (Italy)

Author keywords

Ergodic mean field games; Fractional Kolmogorov Fokker Planck equation; Fractional viscous Hamilton Jacobi equation

Indexed keywords

EID: 85040517831     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2017.10.013     Document Type: Article

References (29)

1. Applebaum, D., Lévy Processes and Stochastic Calculus. second edition Cambridge Studies in Advanced Mathematics, vol. 116, 2009, Cambridge University Press, Cambridge.
2. Barles, G., Chasseigne, E., Ciomaga, A., Imbert, C., Lipschitz regularity of solutions for mixed integro-differential equations. J. Differ. Equ. 252:11 (2012), 6012–6060.
3. Barles, G., Chasseigne, E., Ciomaga, A., Imbert, C., Large time behavior of periodic viscosity solutions for uniformly parabolic integro-differential equations. Calc. Var. Partial Differ. Equ. 50:1–2 (2014), 283–304.
4. Barles, G., Ley, O., Topp, E., Lipschitz regularity for integro-differential equations with coercive Hamiltonians and application to large time behavior. Nonlinearity 30:2 (2017), 703–734.
5. Barrios, B., Figalli, A., Valdinoci, E., Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces. Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 13:3 (2014), 609–639.
6. Basna, R., Hilbert, A., Kolokoltsov, V.N., An approximate Nash equilibrium for pure jump Markov games of mean-field-type on continuous state space. arXiv:1605.05073, 2016.
7. Benazzoli, C., Campi, L., Di Persio, L., Mean-field games with controlled jumps. arXiv:1703.01919, 2017.
8. Bensoussan, A., Frehse, J., Yam, P., Mean Field Games and Mean Field Type Control Theory. SpringerBriefs in Mathematics, 2013, Springer, New York.
9. Bogdan, K., Jakubowski, T., Estimates of heat kernel of fractional Laplacian perturbed by gradient operators. Commun. Math. Phys. 271:1 (2007), 179–198.
10. Borwein, J.M., Vanderwerff, J.D., Convex Functions: Constructions, Characterizations and Counterexamples. Encyclopedia of Mathematics and Its Applications, vol. 109, 2010, Cambridge University Press, Cambridge.
11. Briani, A., Cardaliaguet, P., Stable solutions in potential mean field game systems. arXiv:1612.01877, 2016.
12. Caffarelli, L., Silvestre, L., Regularity results for nonlocal equations by approximation. Arch. Ration. Mech. Anal. 200:1 (2011), 59–88.
13. Capuzzo Dolcetta, I., Leoni, F., Porretta, A., Hölder estimates for degenerate elliptic equations with coercive Hamiltonians. Trans. Am. Math. Soc. 362:9 (2010), 4511–4536.
14. Cardaliaguet, P., Graber, P.J., Porretta, A., Tonon, D., Second order mean field games with degenerate diffusion and local coupling. NoDEA Nonlinear Differ. Equ. Appl. 22:5 (2015), 1287–1317.
15. Ciomaga, A., On the strong maximum principle for second-order nonlinear parabolic integro-differential equations. Adv. Differ. Equ. 17:7–8 (2012), 635–671.
16. Cirant, M., Multi-population mean field games systems with Neumann boundary conditions. J. Math. Pures Appl. (9) 103:5 (2015), 1294–1315.
17. Cirant, M., Stationary focusing mean-field games. Commun. Partial Differ. Equ. 41:8 (2016), 1324–1346.
18. Cont, R., Tankov, P., Financial Modelling with Jump Processes. Chapman & Hall/CRC Financial Mathematics Series, 2004, Chapman & Hall/CRC, Boca Raton, FL.
19. p-estimates for a class of non-local elliptic equations. J. Funct. Anal. 262:3 (2012), 1166–1199.
20. Gomes, D.A., Pimentel, E.A., Voskanyan, V., Regularity Theory for Mean-Field Game Systems. SpringerBriefs in Mathematics, 2016, Springer, Cham.
21. Huang, M., Malhamé R.P., Caines, P.E., Large population stochastic dynamic games: closed-loop McKean–Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6:3 (2006), 221–251 http://projecteuclid.org/euclid.cis/1183728987.
22. Lasry, J.-M., Lions, P.-L., Mean field games. Jpn. J. Math. 2:1 (2007), 229–260.
23. Lions, J.-L., Magenes, E., Problemi ai limiti non omogenei. III. Ann. Sc. Norm. Super. Pisa (3) 15 (1961), 41–103.
24. Mészáros, A.R., Silva, F.J., A variational approach to second order mean field games with density constraints: the stationary case. J. Math. Pures Appl. (9) 104:6 (2015), 1135–1159.
25. Petrosyan, A., Pop, C.A., Optimal regularity of solutions to the obstacle problem for the fractional Laplacian with drift. J. Funct. Anal. 268:2 (2015), 417–472.
26. Rockafellar, R.T., Integral Functionals, Normal Integrands and Measurable Selections. Lecture Notes in Math., vol. 543, 1976, 157–207.
27. Roncal, L., Stinga, P.R., Fractional Laplacian on the torus. Commun. Contemp. Math., 18(3), 2016, 1550033.
28. Roncal, L., Stinga, P.R., Transference of fractional Laplacian regularity. Special Functions, Partial Differential Equations, and Harmonic Analysis, 2014, 203–212.
29. Triebel, H., Theory of Function Spaces. Monographs in Mathematics, vol. 78, 1983, Birkhäuser Verlag, Basel.