|
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Литература
|
|
| |
| 1. |
L. Ambrosio, B. Kirchheim, “Currents in metric spaces”, Acta Math., 185 (2000), 1–80 |
| 2. |
M. J. Beckmann, “A continuous model of transportation”, Econometrica, 20 (1952), 643–660 |
| 3. |
F. Benmansour, G. Carlier, G. Peyré, F. Santambrogio, “Numerical approximation of continuous traffic congestion equilibria”, Netw. Heterog. Media, 4 (2009), 605–623 |
| 4. |
M. Bernot, V. Caselles, J.-M. Morel, Optimal transportation networks. Models and theory, Lecture Notes in Math., 1955, Springer-Verlag, Berlin, 2009 |
| 5. |
G. Bouchitté, G. Buttazzo, “Characterization of optimal shapes and masses through Monge–Kantorovich equation”, J. Eur. Math. Soc., 3 (2001), 139–168 |
| 6. |
G. Bouchitté, G. Buttazzo, L. De Pascale, “The Monge–Kantorovich problem for distributions and applications”, J. Convex Anal., 17 (2010), 925–943 |
| 7. |
G. Bouchitté, T. Champion, C. Jimenez, “Completion of the space of measures in the Kantorovich norm”, Riv. Mat. Univ. Parma, 4 (2005), 127–139 |
| 8. |
L. Brasco, G. Carlier, “Congested traffic equilibria and degenerate anisotropic PDEs”, Dyn Games Appl., 2013 (to appear); available at http://cvgmt.sns.it/paper/1993/ |
| 9. |
L. Brasco, G. Carlier, On certain anisotropic elliptic equations arising in congested optimal transport: local gradient bounds, Preprint available at http://cvgmt.sns.it/paper/1890/, 2012 |
| 10. |
L. Brasco, G. Carlier, F. Santambrogio, “Congested traffic dynamics, weak flows and very degenerate elliptic equations”, J. Math. Pures Appl., 93 (2010), 652–671 |
| 11. |
H. Brezis, J. M. Coron, E. Lieb, “Harmonic maps with defects”, Commun. Math. Phys., 107 (1986), 649–705 |
| 12. |
G. Carlier, C. Jimenez, F. Santambrogio, “Optimal transportation with traffic congestion and Wardrop equilibria”, SIAM J. Control Optim., 47 (2008), 1330–1350 |
| 13. |
B. Dacorogna, J. Moser, “On a partial differential equation involving the Jacobian determinant”, Annales del' I. H. P. Anal. non linéaire, 7 (1990), 1–26 |
| 14. |
C. Dellacherie, P.-A. Meyer, Probabilities and potentials, North-Holland Mathematics Studies, 29, North-Holland Publishing Co., Amsterdam–New York, 1978 |
| 15. |
L. De Pascale, A. Pratelli, “Regularity properties for Monge transport density and for solutions of some shape optimization problems”, Calc. Var. Partial Differential Equations, 14 (2002), 249–274 |
| 16. |
R. J. DiPerna, P.-L. Lions, “Ordinary differential equations, transport theory and Sobolev spaces”, Invent. Math., 98 (1989), 511–547 |
| 17. |
I. Ekeland, Convexity methods in Hamiltonian mechanics, Springer-Verlag, 1990 |
| 18. |
L. C. Evans, W. Gangbo, Differential equations methods for the Monge–Kantorovich mass transfer problem, Mem. Amer. Math. Soc., 137, no. 653, 1999 |
| 19. |
H. Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, 153, Springer-Verlag, 1969 |
| 20. |
M. Feldman, R. McCann, “Uniqueness and transport density in Monges's mass transportation problem”, Calc. Var. Partial Differential Equations, 15 (2004), 81–113 |
| 21. |
M. Giaquinta, G. Modica, J. Souček, Cartesian currents in the calculus of variations, v. I, Modern Surveys in Mathematics, 37, Springer-Verlag, 1998 |
| 22. |
L. Hanin, “Duality for general Lipschitz classes and applications”, Proc. London Math. Soc., 75 (1997), 134–156 |
| 23. |
R. Hardt, T. Rivière, “Connecting topological Hopf singularities”, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 5 (2003), 287–344 |
| 24. |
L. Kantorovich, “On the translocation of masses”, Dokl. Akad. Nauk. SSSR, 37 (1942), 227–229 |
| 25. |
J. Maly, Non-absolutely convergent integrals with respect to distributions, Preprint MATH-KMA-2011/374 http://msekce.karlin.mff.cuni.cz/ms-preprints/kma-preprints/, 2011 |
| 26. |
J. Moser, “On the volume elements on a manifold”, Trans. Am. Math. Soc., 120 (1965), 286–294 |
| 27. |
E. Paolini, E. Stepanov, “Decomposition of acyclic normal currents in a metric space”, J. Funct. Anal., 263 (2012), 3358–3390 |
| 28. |
E. Paolini, E. Stepanov, “Structure of metric cycles and normal one-dimensional currents”, J. Funct. Anal., 264 (2013), 1269–1295 |
| 29. |
E. Paolini, E. Stepanov, “Optimal transportation networks as flat chains”, Interfaces Free Bound., 8 (2006), 393–436 |
| 30. |
M. Petrache, Notes on a slice distance for singular $L^p$-bundles, Preprint, available at http://cvgmt.sns.it/paper/1752/, 2012 |
| 31. |
M. Petrache, Interior partial regularity for minimal $L^p$-vectorfields with integer fluxes, Preprint, available at http://cvgmt.sns.it/paper/1751/, 2012 |
| 32. |
M. Petrache, T. Rivière, “Weak closure of singular abelian $L^p$-bundles in 3 dimensions”, Geom. Funct. Anal., 21 (2011), 1419–1442 |
| 33. |
A. C. Ponce, “On the distributions of the form $\sum_i\delta_{p_i}-\delta_{n_i}$”, J. Funct. Anal., 210 (2004), 391–435 |
| 34. |
T. Rivière, “Lines vortices in the $U(1)$-Higgs model”, ESAIM Control Optim. Calc. Var., 1 (1996), 77–167 |
| 35. |
E. Sandier, “Ginzburg-Landau minimizers from $\mathbb R^{n+1}$ to $\mathbb R^n$ and minimal connections”, Indiana Univ. Math. J., 50 (2001), 1807–1844 |
| 36. |
S. K. Smirnov, “Decomposition of solenoidal vector charges into elementary solenoids and the structure of normal one-dimensional currents”, St.-Petersburg Math. J., 5:4 (1994), 841–867 |
| 37. |
G. Strang, “$L^1$ and $L^\infty$ approximation of vector fields in the plane”, Lecture Notes in Num. Appl. Anal., 5, 1982, 273–288 |
| 38. |
T. Valkonen, “Optimal transportation networks and stations”, Interfaces Free Bound., 11 (2009), 569–597 |
| 39. |
C. Villani, Topics in optimal transportation, Graduate Studies in Mathematics, 58, American Mathematical Society, Providence, RI, 2003 |
| 40. |
J. G. Wardrop, “Some theoretical aspects of road traffic research”, Proc. Inst. Civ. Eng., 2 (1952), 325–378 |