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Maximal abelian torsion subgroups of Diff( C,0)
An equivalent path functional formulation of branched transportation problems
1. | Dipartimento di Matematica e Applicazioni, Università di Napoli "Federico II", Complesso di Monte S. Angelo, Via Cintia, 80126 Napoli, Italy |
2. | Laboratoire de Mathématiques d'Orsay, UMR CNRS 8628, Faculté des Sciences, Université Paris-Sud XI, 91405 Orsay Cedex, France |
References:
[1] |
L. Ambrosio, N. Gigli and G. Savaré, "Gradient Flows in Metric Spaces and in the Space of Probability Measures," 2nd edition, Lectures in Mathematics ETH, Zürich, Birkhäuser Verlag, Basel, 2008. |
[2] |
L. Ambrosio and P. Tilli, "Selected topics on 'Analysis in Metric Spaces'," Appunti dei corsi tenuti da docenti della Scuola, Scuola Normale Superiore, Pisa, 2000. |
[3] |
M. Bernot, V. Caselles and J.-M. Morel, Traffic plans, Publ. Mat., 49 (2005), 417-451. |
[4] |
M. Bernot, V. Caselles and J.-M. Morel, The structure of branched transportation networks, Calc. Var. Partial Differential Equations, 2 (2008), 279-371.
doi: 10.1007/s00526-007-0139-0. |
[5] |
M. Bernot, V. Caselles and J.-M. Morel, "Optimal Transportation Networks. Models and Theory," Lecture Notes in Mathemathics, 1955, Springer-Verlag, Berlin, 2009. |
[6] |
M. Bernot and A. Figalli, Synchronized traffic plans and stability of optima, ESAIM Control Optim. Calc. Var., 14 (2008), 864-878.
doi: 10.1051/cocv:2008012. |
[7] |
S. Bianchini and A. Brancolini, Estimates on path functionals over Wasserstein spaces, SIAM J. Math. Anal., 42 (2010), 1179-1217.
doi: 10.1137/100782693. |
[8] |
A. Brancolini, G. Buttazzo and F. Santambrogio, Path functionals over Wasserstein spaces, J. Eur. Math. Soc., 8 (2006), 415-434.
doi: 10.4171/JEMS/61. |
[9] |
A. Brancolini and S. Solimini, On the Hölder regularity of the landscape function,, accepted on Interfaces Free Bound., ().
|
[10] |
L. Brasco, Curves of minimal action over metric spaces, Ann. Mat. Pura Appl., 189 (2010), 95-125.
doi: 10.1007/s10231-009-0102-0. |
[11] |
C. Dellacherie and P.-A. Meyer, "Probabilités et Potentiel" (French) [Probabilities and Potential], Chapitres I à IV. Édition entièrement refondue, Publications de l'Institut de Mathématique de l'Université de Strasbourg, No. XV, Actualités Scientifiques et Industrielles, 1372, Hermann, Paris, 1975. |
[12] |
E. N. Gilbert and H. O. Pollak, Steiner minimal trees, SIAM J. Appl. Math., 16 (1968), 1-29.
doi: 10.1137/0116001. |
[13] |
S. Lisini, Characterization of absolutely continuous curves in Wasserstein spaces, Calc. Var. Partial Differential Equations, 28 (2007), 85-120.
doi: 10.1007/s00526-006-0032-2. |
[14] |
F. Maddalena, J.-M. Morel and S. Solimini, A variational model of irrigation patterns, Interfaces Free Bound., 5 (2003), 391-415.
doi: 10.4171/IFB/85. |
[15] |
F. Santambrogio, Optimal channel networks, landscape function and branched transport, Interfaces Free Bound., 9 (2007), 149-169. |
[16] |
C. Villani, "Topics in Optimal Transportation," Graduate Studies in Mathematics, 58, American Mathematical Society, Providence, RI, 2003. |
[17] |
Q. Xia, Optimal paths related to transport problems, Commun. Contemp. Math., 5 (2003), 251-279.
doi: 10.1142/S021919970300094X. |
show all references
References:
[1] |
L. Ambrosio, N. Gigli and G. Savaré, "Gradient Flows in Metric Spaces and in the Space of Probability Measures," 2nd edition, Lectures in Mathematics ETH, Zürich, Birkhäuser Verlag, Basel, 2008. |
[2] |
L. Ambrosio and P. Tilli, "Selected topics on 'Analysis in Metric Spaces'," Appunti dei corsi tenuti da docenti della Scuola, Scuola Normale Superiore, Pisa, 2000. |
[3] |
M. Bernot, V. Caselles and J.-M. Morel, Traffic plans, Publ. Mat., 49 (2005), 417-451. |
[4] |
M. Bernot, V. Caselles and J.-M. Morel, The structure of branched transportation networks, Calc. Var. Partial Differential Equations, 2 (2008), 279-371.
doi: 10.1007/s00526-007-0139-0. |
[5] |
M. Bernot, V. Caselles and J.-M. Morel, "Optimal Transportation Networks. Models and Theory," Lecture Notes in Mathemathics, 1955, Springer-Verlag, Berlin, 2009. |
[6] |
M. Bernot and A. Figalli, Synchronized traffic plans and stability of optima, ESAIM Control Optim. Calc. Var., 14 (2008), 864-878.
doi: 10.1051/cocv:2008012. |
[7] |
S. Bianchini and A. Brancolini, Estimates on path functionals over Wasserstein spaces, SIAM J. Math. Anal., 42 (2010), 1179-1217.
doi: 10.1137/100782693. |
[8] |
A. Brancolini, G. Buttazzo and F. Santambrogio, Path functionals over Wasserstein spaces, J. Eur. Math. Soc., 8 (2006), 415-434.
doi: 10.4171/JEMS/61. |
[9] |
A. Brancolini and S. Solimini, On the Hölder regularity of the landscape function,, accepted on Interfaces Free Bound., ().
|
[10] |
L. Brasco, Curves of minimal action over metric spaces, Ann. Mat. Pura Appl., 189 (2010), 95-125.
doi: 10.1007/s10231-009-0102-0. |
[11] |
C. Dellacherie and P.-A. Meyer, "Probabilités et Potentiel" (French) [Probabilities and Potential], Chapitres I à IV. Édition entièrement refondue, Publications de l'Institut de Mathématique de l'Université de Strasbourg, No. XV, Actualités Scientifiques et Industrielles, 1372, Hermann, Paris, 1975. |
[12] |
E. N. Gilbert and H. O. Pollak, Steiner minimal trees, SIAM J. Appl. Math., 16 (1968), 1-29.
doi: 10.1137/0116001. |
[13] |
S. Lisini, Characterization of absolutely continuous curves in Wasserstein spaces, Calc. Var. Partial Differential Equations, 28 (2007), 85-120.
doi: 10.1007/s00526-006-0032-2. |
[14] |
F. Maddalena, J.-M. Morel and S. Solimini, A variational model of irrigation patterns, Interfaces Free Bound., 5 (2003), 391-415.
doi: 10.4171/IFB/85. |
[15] |
F. Santambrogio, Optimal channel networks, landscape function and branched transport, Interfaces Free Bound., 9 (2007), 149-169. |
[16] |
C. Villani, "Topics in Optimal Transportation," Graduate Studies in Mathematics, 58, American Mathematical Society, Providence, RI, 2003. |
[17] |
Q. Xia, Optimal paths related to transport problems, Commun. Contemp. Math., 5 (2003), 251-279.
doi: 10.1142/S021919970300094X. |
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