Optimal multiphase transportation with prescribed momentum

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 8, Issue , 2002, Pages 287-343

  Brenier, Yann ^a   Puel, Marjolaine ^b  

^a UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

Electrodynamics; Multiphase flow; Optimal transportation

Indexed keywords

ELECTRODYNAMICS; METHOD OF MOMENTS; OPTIMAL SYSTEMS; PROBLEM SOLVING;

MONGE-KANTOROVICH; OPTIMAL TRANSPORTATION;

MULTIPHASE FLOW;

EID: 3042832274     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2002024     Document Type: Article

References (25)

1. F. Barthe, Optimal Young's inequality and its converse: A simple proof. Geom. Funct. Anal. 8 (1998) 234-242.
2. J.-D. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84 (2000) 375-393.
3. M. Born and L. Infeld, Foundations of the new field theory. Proc. Roy. Soc. London A 144 (1934) 425-451.
4. G. Bouchitté and G. Buttazzo, Characterization of optimal shapes and masses through Monge-Kantorovich equation. J. Eur. Math. Soc. (JEMS) 3 (2001) 139-168.
5. Y. Brenier, A combinatorial algorithm for the Euler equations of incompressible flows, in Proc. of the Eighth International Conference on Computing Methods in Applied Sciences and Engineering. Versailles (1987). Comput. Methods Appl. Mech. Engrg. 75 (1989) 325-332.
6. Y. Brenier, Décomposition polaire et réarrangement monotone des champs de vecteurs. C. R. Acad. Sci. Paris Sér. I Math. 305 (1987) 805-808.
7. Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions. Comm. Pure Appl. Math. 64 (1991) 375-417.
8. Y. Brenier, A homogenized model for vortex sheets. Arch. Rational Mech. Anal. 138 (1997) 319-353.
9. Y. Brenier, Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations. Comm. Pure Appl. Math. 52 (1999) 411-452.
10. Y. Brenier, Extension of the Monge-Kantorovich theory to classical electrodynamics. Summer School on mass transportation methods in kinetic theory and hydrodynamics. Ponta Delgada, Azores, Portugal (2000).
11. H. Brézis, Analyse fonctionnelle. Masson, Paris (1974).
12. L.A. Caffarelli, Boundary regularity of maps with convex potentials. Ann. of Math. (2) 144 (1996) 453-496.
13. M.J. Cullen and R.J. Purser, An extended Lagrangian theory of semigeostrophic frontogenesis. J. Atmos. Sci. 41 (1984) 1477-1497.
14. L.C. Evans and W. Gangbo, Differential equations methods for the Monge-Kantorovich mass transfer problem. Mem. Amer. Math. Soc. 137 (1999).
15. W. Gangbo and R.J. McCann, The geometry of optimal transportation. Acta Math. 177 (1996) 113-161.
16. D. Kinderlehrer, R. Jordan and F. Otto, The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29 (1998) 1-17.
17. L.V. Kantorovich, On a problem of Monge. Uspekhi Mat. Nauk. 3 (1948) 225-226.
18. R.J. McCann, A convexity principle for interacting gases. Adv. Math. 128 (1997) 153-179.
19. F. Otto, Viscous fingering: An optimal bound on the growth rate of the mixing zone. SIAM J. Appl. Math. 57 (1997) 982-990.
20. F. Otto, The geometry of dissipative evolution equations: The porous medium equation. Comm. Partial Differential Equations 26 (2001) 101-174
21. F. Otto and C. Villani, Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality. J. Funct. Anal. 173 (2000) 361-400.
22. A.V. Pogorelov, The Minkowski multidimensional problem. John Wiley, New York-Toronto-London, Ser. Ser. in Math. (1978).
23. S.T. Rachev and L. Rüschendorf, Mass transportation problems, Vols. I and II. Probability and its Applications. Springer-Verlag.
24. G. Strang, Introduction to applied mathematics. Wellesley-Cambridge Press, Wellesley, MA (1986).
25. V.N. Sudakov, Geometric problems in the theory of infinite-dimensional probability distributions. Proc. Steklov Inst. 141 (1979) 1-178.