Constructing a Relativistic Heat Flow by Transport Time Steps
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2539-2580.
@article{AIHPC_2009__26_6_2539_0,
     author = {Mccann, Robert J. and Puel, Marjolaine},
     title = {Constructing a {Relativistic} {Heat} {Flow} by {Transport} {Time} {Steps}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {2539--2580},
     publisher = {Elsevier},
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     number = {6},
     year = {2009},
     doi = {10.1016/j.anihpc.2009.06.006},
     mrnumber = {2569908},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2009.06.006/}
}
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Mccann, Robert J.; Puel, Marjolaine. Constructing a Relativistic Heat Flow by Transport Time Steps. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2539-2580. doi : 10.1016/j.anihpc.2009.06.006. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.06.006/

[1] Agueh Martial, Existence of Solutions to Degenerate Parabolic Equations Via the Monge-Kantorovich Theory, Adv. Differential Equations 10 (3) (2005) 309-360. | MR | Zbl

[2] Luigi Ambrosio, Steepest descent flows and applications to spaces of probability measures, Lectures Notes, Santander, July 2004. | Zbl

[3] Ambrosio Luigi, Gigli Nicola, Savaré Giuseppe, Gradient Flows in Metric Spaces and in the Spaces of Probability Measures, Lectures Math. ETH Zurich, Birkhäuser Verlag, Basel, 2005. | MR | Zbl

[4] Luigi Ambrosio, Aldo Pratelli, Existence and Stability Results in the L 1 Theory of Optimal Transportation, Lecture Notes in Math. | Zbl

[5] Ambrosio Luigi, Tilli Paolo, Topics on Analysis in Metric Spaces, Oxford Lecture Ser. Math. Appl., vol. 25, Oxford University Press, Oxford, 2004. | MR | Zbl

[6] Anzellotti Gianni, Pairing Between Measures and Bounded Functions and Compensated Compactness, Ann. Mat. Pura Appl. (4) 135 (1983) 293-318. | MR | Zbl

[7] Andreu Fuensanta, Caselles Vicent, Mazón José M., Existence and Uniqueness of Solution for a Parabolic Quasilinear Problem for Linear Growth Functionals With L 1 Data, Math. Ann. 322 (2002) 139-206. | MR | Zbl

[8] Andreu Fuensanta, Caselles Vicent, Mazón José M., Parabolic Quasilinear Equations Minimizing Linear Growth Functionals, Progr. Math., vol. 223, Birkhäuser Verlag, 2004. | MR | Zbl

[9] Andreu Fuensanta, Caselles Vicent, Mazón José M., A Strongly Degenerate Quasilinear Equation: the Elliptic Case, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 3 (3) (2004) 555-587. | Numdam | MR | Zbl

[10] Andreu Fuensanta, Caselles Vicent, Mazón José M., A Strong Degenerate Quasilinear Equation: the Parabolic Case, Arch. Ration. Mech. Anal. (2005). | MR | Zbl

[11] Andreu Fuensanta, Caselles Vicent, Mazón José M., A Strongly Degenerate Quasilinear Elliptic Equation, Nonlinear Anal. 61 (2005) 637-669.

[12] Andreu Fuensanta, Caselles Vicent, Mazón José M., The Cauchy Problem for a Strong Degenerate Quasilinear Equation, J. Eur. Math. Soc. (JEMS) 7 (2005) 361-393. | MR | Zbl

[13] Fuensanta Andreu, Vicent Caselles, José M. Mazón, Salvador Moll, The speed of propagation of the support of solutions of a tempered diffusion equation, preprint.

[14] Brenier Yann, Extended Monge-Kantorovich Theory, in: Optimal Transportation and Applications, Martina Franca, 2001, Lecture Notes in Math., vol. 1813, Springer, Berlin, 2003, pp. 91-121. | MR | Zbl

[15] Brezis Haim, Analyse Fonctionnelle Et Ses Applications, Masson, 1983. | MR | Zbl

[16] Brezis Haim, Opérateurs Maximaux Monotones Et Semi-Groupes De Contractions Dans Les Espaces De Hilbert, North-Holland Math. Stud., vol. 5, North-Holland Publishing Co./American Elsevier Publishing Co., Inc., Amsterdam, London/New York, 1973, (in French). | MR | Zbl

[17] Caffarelli Luis A., Boundary Regularity of Maps With Convex Potentials. II, Ann. of Math. (2) 144 (3) (1996) 453-496. | MR | Zbl

[18] Carrillo Jose Antonio, Toscani Giuseppe, Wasserstein Metric and Large-Time Asymptotics of Nonlinear Diffusion Equations, in: New Trends in Mathematical Physics, World Sci. Publ., Hackensack, NJ, 2005, pp. 234-244, (in honor of the Salvatore Rionero 70th birthday). | MR | Zbl

[19] Caselles Vicent, Convergence of the “relativistic” Heat Equation to the Heat Equation as c, Publ. Mat. 51 (1) (2007) 121-142. | MR | Zbl

[20] Chertock Alina, Kurganov Alexander, Rosenau Philip, Formation of Discontinuities in Flux-Saturated Degenerate Parabolic Equations, Nonlinearity 16 (2003) 1875-1898. | MR | Zbl

[21] Cordero-Erausquin Dario, Non-Smooth Differential Properties of Optimal Transport, in: Recent Advances in the Theory and Applications of Mass Transport, Contemp. Math., vol. 353, Amer. Math. Soc., Providence, RI, 2004, pp. 61-71. | MR | Zbl

[22] Dal Maso Gianni, Integral Representation on BV ω of Γ-Limits of Variational Integrals, Manuscripta Math. 30 (1980) 387-416. | MR | Zbl

[23] De Cicco Virginia, Fusco Nicola, Verde Anna, On L 1 -Lower Semicontinuity in BV, J. Convex Anal. 12 (1) (2005) 173-185. | MR | Zbl

[24] Dunford Nelson, Schwartz Jaco, Linear Operators, Interscience Publishers, New York, 1958. | MR | Zbl

[25] Evans Lawrence C., Weak Convergence Methods for Nonlinear Partial Differential Equations, published for the Conference Board of the Mathematical Sciences, Washington, DC, CBMS Reg. Conf. Ser. Math., vol. 74, Amer. Math. Soc., Providence, RI, 1990. | MR | Zbl

[26] Evans Lawrence C., Gangbo Wilfrid, Differential Equation Methods for the Monge Kantorovich Mass Transfer, Mem. Amer. Math. Soc. 653 (1999). | MR | Zbl

[27] Evans Lawrence C., Gariepy Ronald F., Measure Theory and Fine Properties of Functions, Stud. Adv. Math., CRC Press, 1992. | MR | Zbl

[28] Gangbo Wilfrid, Mccann Robert J., Optimal Maps in Monge's Mass Transport Problem, C. R. Acad. Sci. Paris Sér. I Math. 321 (12) (1995) 1653-1658. | MR | Zbl

[29] Gangbo Wilfrid, Mccann Robert J., The Geometry of Optimal Transportation, Acta Math. 177 (2) (1996) 113-161. | MR | Zbl

[30] Jordan Richard, Kinderlehrer David, Otto Felix, The Variational Formulation of the Fokker-Planck Equation, SIAM J. Math. Anal. 29 (1) (1998) 1-17. | MR | Zbl

[31] Robert Kohn, Roger Temam, Dual Spaces of Stresses and Strains, With Applications to Hencky Plasticity, Appl. Math. Optim. 10 (1) (1983) 1-35. | MR | Zbl

[32] Lions Jacques-Louis, Quelques Methodes De Résolution Des Problèmes Aux Limites Non Linéaires, Dunod, 1969. | MR | Zbl

[33] Loeper Grégoire, On the Regularity of the Polar Factorization for Time Dependent Maps, Calc. Var. Partial Differential Equations 22 (3) (2005) 343-374. | MR | Zbl

[34] Ma Xi-Nan, Trudinger Neil S., Wang Xu-Jia, Regularity of Potential Functions of the Optimal Transportation Problem, Arch. Ration. Mech. Anal. 177 (2) (2005) 151-183. | MR | Zbl

[35] Mccann Robert J., A Convexity Principle for Interacting Gases, Adv. Math. 128 (1997) 153-179. | MR | Zbl

[36] Mccann Robert J., Exact Solutions to the Transportation Problem on the Line, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 455 (1984) (1999) 1341-1380. | MR | Zbl

[37] Mihalas D., Mihalas B., Foundations of Radiation Hydrodynamics, Oxford University Press, 1984. | MR | Zbl

[38] Felix Otto, Doubly degenerate diffusion equations as steepest descent, preprint, 1996. | MR

[39] Rachev Svetlozar T., Rüschendorf Ludger, Mass Transportation Problems, Vols. I. and II, Probab. Appl. (N. Y.), Springer-Verlag, New York, 1998. | MR | Zbl

[40] Rosenau Philip, Tempered Diffusion: a Transport Process With Propagating Fronts and Initial Delay, Phys. Rev. A 46 (1992) 7371-7374.

[41] Simon Jacques, Compact sets in the space L p (0,T;B), Ann. Mat. Pura Appl. 146 (1987) 65-96. | MR | Zbl

[42] Temam Roger, Navier-Stokes Equation. Theory and Numerical Analysis, Stud. Math. Appl., vol. 2, third ed., North-Holland Publishing Co., Amsterdam, 1984. | MR | Zbl

[43] Villani Cedric, Topics in Optimal Transportation, Grad. Stud. Math., vol. 58, Amer. Math. Soc., 2003. | MR | Zbl

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