Homogenization for a class of integral functionals in spaces of probability measures

Advances in Mathematics

Volumn 230, Issue 3, 2012, Pages 1124-1173

  Gangbo, Wilfrid ^a   Tudorascu, Adrian ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b WEST VIRGINIA UNIVERSITY   (United States)

Author keywords

convergence; Effective Lagrangians; Homogenization; Mass transfer; Wasserstein metric

Indexed keywords

EID: 84859915674     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2012.03.005     Document Type: Article

References (19)

1. Alastuey A. Mean-field kinetic theory of a classical electron gas in a periodic potential. I. Formal solution of the Vlasov equation. J. Stat. Phys. 1987, 48:839-871.
2. Ambrosio L., Gigli N., Savaré G. Gradient flows in metric spaces and the Wasserstein spaces of probability measures. Lectures in Mathematics 2005, Birkhäuser, ETH, Zurich.
3. Ayuso B., Carrillo A.J., Shu C.W. Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system. Kinet. Relat. Models 2011, 4:955-989.
4. Brenier Y. Polar factorization and monotone rearrangement of vector-valued functions. Comm. Pure Appl. Math. 1991, 44:375-417.
5. Evans L.C., Gariepy R.F. Measure Theory and Fine Properties of Functions 1992, CRC Press.
6. A. Fathi, Weak KAM theory in Lagrangian dynamics, Preliminary Version, Lecture Notes, 2003.
7. Gangbo W., Kim H.K., Pacini T. Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems. Mem. Amer. Math. Soc. 2011, 211(993).
8. Gangbo W., McCann R. The geometry of optimal transportation. Acta Math. 1996, 177:113-161.
9. Gangbo W., Nguyen T., Tudorascu A. Hamilton-Jacobi equations in the Wasserstein space. Methods Appl. Anal. 2008, 15(2):155-184.
10. Gangbo W., Nguyen T., Tudorascu A. Euler-Poisson systems as action minimizing paths in the Wasserstein space. Arch. Ration. Mech. Anal. 2009, 192(3):419-452.
11. W. Gangbo, A. Tudorascu, A weak KAM theorem; from finite to infinite dimension, Edizioni Della Normale, Scuola Normale Superiore Pisa, 2010.
12. Gangbo W., Tudorascu A. Lagrangian dynamics on an infinite-dimensional torus; a weak KAM theorem. Adv. Math. 2010, 224(1):260-292.
13. Guo Y. The Vlasov-Poisson-Landau system in a periodic box. J. Amer. Math. Soc. 2011, 10.1090/S0894-0347-2011-00722-4.
14. Herrero M.A., Zuazua E. Current Trends in Applied Mathematics 1996, Editorial Complutense.
15. P.L. Lions, G. Papanicolaou, S.R.S. Varadhan, Homogenization of Hamilton-Jacobi equations, CCA, 1988 (unpublished).
16. Muller S. Homogenization of nonconvex integral functionals and elastic materials. Arch. Ration. Mech. Anal. 1987, 99:189-212.
17. Nguyen T., Tudorascu A. Pressureless Euler/Euler-Poisson systems via adhesion dynamics and scalar conservation laws. SIAM J. Math. Anal. 2008, 40(2):754-775.
18. Tudorascu A. On the velocities of flows consisting of cyclically monotone maps. Indiana Univ. Math. J. 2010, 59(3):929-956.
19. E W. A class of homogenization problems in the calculus of variations. Comm. Pure Appl. Math. 1991, XLIV:733-759.