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Volumn 67, Issue 3, 2014, Pages 408-463

Weak KAM Theory on the Wasserstein Torus with Multidimensional Underlying Space

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EID: 84892372400     PISSN: 00103640     EISSN: 10970312     Source Type: Journal    
DOI: 10.1002/cpa.21492     Document Type: Article
Times cited : (21)

References (19)
  • 1
    • 37649010339 scopus 로고    scopus 로고
    • Hamiltonian ODEs in the Wasserstein space of probability measures
    • doi:10.1002/cpa.20188
    • Ambrosio, L.; Gangbo, W. Hamiltonian ODEs in the Wasserstein space of probability measures. Comm. Pure Appl. Math. 61 (2008), no. 1, 18-53. doi:10.1002/cpa.20188
    • (2008) Comm. Pure Appl. Math , vol.61 , Issue.1 , pp. 18-53
    • Ambrosio, L.1    Gangbo, W.2
  • 2
    • 33746157912 scopus 로고    scopus 로고
    • Gradient flows in metric spaces and in the Wasserstein spaces of probability measures. Lectures in Mathematics ETH Zurich
    • Ambrosio, L.; Gigli, N.; Savaré, G. Gradient flows in metric spaces and in the Wasserstein spaces of probability measures. Lectures in Mathematics ETH Zurich. Birkhäuser, Basel, 2005.
    • (2005) Birkhäuser, Basel
    • Ambrosio, L.1    Gigli, N.2    Savaré, G.3
  • 3
    • 84876132856 scopus 로고    scopus 로고
    • Sticky particle dynamics with interactions
    • (9), doi:10.1016/j.matpur.2012.09.013
    • Brenier, Y.; Gangbo, W.; Savaré, G.; Westdickenberg, M. Sticky particle dynamics with interactions. J. Math. Pures Appl. (9) 99 (2013), no. 5, 577-617. doi:10.1016/j.matpur.2012.09.013
    • (2013) J. Math. Pures Appl , vol.99 , Issue.5 , pp. 577-617
    • Brenier, Y.1    Gangbo, W.2    Savaré, G.3    Westdickenberg, M.4
  • 4
    • 0000466871 scopus 로고    scopus 로고
    • Periodic homogenization of Hamilton-Jacobi equations: additive eigenvalues and variational formula
    • doi:10.1512/iumj.1996.45.1145
    • Concordel, M. C. Periodic homogenization of Hamilton-Jacobi equations: additive eigenvalues and variational formula. Indiana Univ. Math. J. 45 (1996), no. 4, 1095-1117. doi:10.1512/iumj.1996.45.1145
    • (1996) Indiana Univ. Math. J , vol.45 , Issue.4 , pp. 1095-1117
    • Concordel, M.C.1
  • 5
    • 0033177753 scopus 로고    scopus 로고
    • Sur le transport de mesures périodiques
    • doi:10.1016/S0764-4442(00)88593-6
    • Cordero-Erausquin, D. Sur le transport de mesures périodiques. C. R. Acad. Sci. Paris Sér. I Math 329 (1999), no. 3, 199-202. doi:10.1016/S0764-4442(00)88593-6
    • (1999) C. R. Acad. Sci. Paris Sér. I Math , vol.329 , Issue.3 , pp. 199-202
    • Cordero-Erausquin, D.1
  • 6
    • 2442713751 scopus 로고    scopus 로고
    • A survey of partial differential equations methods in weak KAM theory
    • doi:10.1002/cpa.20009
    • Evans, L. C. A survey of partial differential equations methods in weak KAM theory. Comm. Pure Appl. Math. 57 (2004), no. 4, 445-480. doi:10.1002/cpa.20009
    • (2004) Comm. Pure Appl. Math , vol.57 , Issue.4 , pp. 445-480
    • Evans, L.C.1
  • 7
    • 84892374193 scopus 로고    scopus 로고
    • Weak KAM theory in Lagrangian dynamics
    • Fathi, A. Weak KAM theory in Lagrangian dynamics. Lecture notes, 2003.
    • (2003) Lecture notes
    • Fathi, A.1
  • 8
    • 84884753138 scopus 로고    scopus 로고
    • On Lagrangian solutions for the semi-geostrophic system with singular data
    • doi:10.1137/120870116
    • Feldman, M.; Tudorascu, A. On Lagrangian solutions for the semi-geostrophic system with singular data. SIAM J. Math. Anal. 45 (2013), no. 3, 1616-1640. doi:10.1137/120870116
    • (2013) SIAM J. Math. Anal , vol.45 , Issue.3 , pp. 1616-1640
    • Feldman, M.1    Tudorascu, A.2
  • 9
    • 84860541260 scopus 로고    scopus 로고
    • Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems
    • vi+77 doi:10.1090/S0065-9266-2010-00610-0
    • Gangbo, W.; Kim, H. K.; Pacini, T. Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems. Mem. Amer. Math. Soc. 211 (2011), no. 993, vi+77 pp. doi:10.1090/S0065-9266-2010-00610-0
    • (2011) Mem. Amer. Math. Soc , vol.211 , Issue.993
    • Gangbo, W.1    Kim, H.K.2    Pacini, T.3
  • 10
    • 0001103156 scopus 로고    scopus 로고
    • The geometry of optimal transportation
    • doi:10.1007/BF02392620
    • Gangbo, W.; McCann, R. J. The geometry of optimal transportation. Acta Math. 177 (1996), no. 2, 113-161. doi:10.1007/BF02392620
    • (1996) Acta Math , vol.177 , Issue.2 , pp. 113-161
    • Gangbo, W.1    McCann, R.J.2
  • 11
    • 77049105922 scopus 로고    scopus 로고
    • Hamilton-Jacobi equations in the Wasserstein space
    • Gangbo, W.; Nguyen, T.; Tudorascu, A. Hamilton-Jacobi equations in the Wasserstein space. Methods Appl. Anal. 15 (2008), no. 2, 155-183.
    • (2008) Methods Appl. Anal , vol.15 , Issue.2 , pp. 155-183
    • Gangbo, W.1    Nguyen, T.2    Tudorascu, A.3
  • 12
    • 67349235555 scopus 로고    scopus 로고
    • Euler-Poisson systems as action-minimizing paths in the Wasserstein space
    • doi:10.1007/s00205-008-0148-y
    • Gangbo, W.; Nguyen, T.; Tudorascu, A. Euler-Poisson systems as action-minimizing paths in the Wasserstein space. Arch. Ration. Mech. Anal. 192 (2009), no. 3, 419-452. doi:10.1007/s00205-008-0148-y
    • (2009) Arch. Ration. Mech. Anal , vol.192 , Issue.3 , pp. 419-452
    • Gangbo, W.1    Nguyen, T.2    Tudorascu, A.3
  • 13
    • 77049089463 scopus 로고    scopus 로고
    • Lagrangian dynamics on an infinite-dimensional torus; a weak KAM theorem
    • doi:10.1016/j.aim.2009.11.005
    • Gangbo W.; Tudorascu, A. Lagrangian dynamics on an infinite-dimensional torus; a weak KAM theorem. Adv. Math. 224 (2010), no. 1, 260-292. doi:10.1016/j.aim.2009.11.005
    • (2010) Adv. Math , vol.224 , Issue.1 , pp. 260-292
    • Gangbo, W.1    Tudorascu, A.2
  • 14
    • 84862864586 scopus 로고    scopus 로고
    • A weak KAM theorem; from finite to infinite dimension
    • CRM Series, Edizioni Della Normale, Pisa
    • Gangbo, W.; Tudorascu, A. A weak KAM theorem; from finite to infinite dimension. Optimal transportation, geometry and functional inequalities, 45-72. CRM Series, 11. Edizioni Della Normale, Pisa, 2010.
    • (2010) Optimal transportation, geometry and functional inequalities , vol.11 , pp. 45-72
    • Gangbo, W.1    Tudorascu, A.2
  • 15
    • 84859915674 scopus 로고    scopus 로고
    • Homogenization for a class of integral functionals in spaces of probability measures
    • doi:10.1016/j.aim.2012.03.005
    • Gangbo, W.; Tudorascu, A. Homogenization for a class of integral functionals in spaces of probability measures. Adv. Math. 230(2012), no. 3, 1124-1173. doi:10.1016/j.aim.2012.03.005
    • (2012) Adv. Math , vol.230 , Issue.3 , pp. 1124-1173
    • Gangbo, W.1    Tudorascu, A.2
  • 16
    • 84860630927 scopus 로고    scopus 로고
    • Second order analysis on (i_2(M),W_2)
    • xii+154 doi:10.1090/S0065-9266-2011-00619-2
    • Gigli, N. Second order analysis on (i_2(M), W_2). Mem. Amer. Math. Soc. 216 (2012), no. 1018, xii+154 pp. doi:10.1090/S0065-9266-2011-00619-2
    • (2012) Mem. Amer. Math. Soc , vol.216 , Issue.1018
    • Gigli, N.1
  • 17
    • 0036556944 scopus 로고    scopus 로고
    • Viscosity solutions of Hamilton-Jacobi equations, and asymptotics for Hamiltonian systems
    • doi:10.1007/s005260100106
    • Gomes, D. A. Viscosity solutions of Hamilton-Jacobi equations, and asymptotics for Hamiltonian systems. Calc. Var. Partial Differential Equations 14 (2002), no. 3, 345-357. doi:10.1007/s005260100106
    • (2002) Calc. Var. Partial Differential Equations , vol.14 , Issue.3 , pp. 345-357
    • Gomes, D.A.1
  • 18
    • 84892363951 scopus 로고    scopus 로고
    • Hamiltonian systems and the calculus of differential forms on the Wasserstein space. Doctoral dissertation
    • Atlanta
    • Kim, H. K. Hamiltonian systems and the calculus of differential forms on the Wasserstein space. Doctoral dissertation. Georgia Institute of Technology, Atlanta, 2008.
    • (2008) Georgia Institute of Technology
    • Kim, H.K.1
  • 19
    • 73249119910 scopus 로고    scopus 로고
    • Topics in optimal transportation. Graduate Studies in Mathematics
    • doi:10.1007/b12016
    • Villani, C. Topics in optimal transportation. Graduate Studies in Mathematics, 58. American Mathematical Society, Providence, R.I., 2003. doi:10.1007/b12016
    • (2003) American Mathematical Society, Providence, R.I , vol.58
    • Villani, C.1


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