Regularity properties for Monge transport density and for solutions of some shape optimization problem

Calculus of Variations and Partial Differential Equations

Volumn 14, Issue 3, 2002, Pages 249-274

  De Pascale, Luigi ^a   Pratelli, Aldo ^b  

^a UNIVERSITY OF PISA   (Italy)

^b SCUOLA NORMALE SUPERIORE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036556947     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s005260100086     Document Type: Article

References (21)

1. L. Ambrosio, Lecture Notes on Optimal Transportation Problems; lectures given in Madeira (Portugal), 2-9 July 2000, preprint.
2. J.-D. Benamou, Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem, Numer. Math., 84 (2000), 375-393.
3. G. Bouchitté, G. Buttazzo, Characterization of optimal shapes and masses through Monge-Kantorovich Equation, J. Eur. Math. Soc. (JEMS) 3, 139-168.
4. G. Bouchitté, G. Buttazzo, P. Seppecher, Energy with Respect to a Measure and Applications to Low Dimensional Structures., Calc.Var., 5 (1997), 37-54.
5. G. Bouchitté, G. Buttazzo, P. Seppecher, Shape optimization solutions via Monge-Kantorovich equation, C.R. Acad. Sci. Paris, 324-I (1997), 1185-1191.
6. L.A. Caffarelli, M. Feldman, R. McCann, Constructing optimal maps in Monge's transport problem as a limit of strictly convex costs, to appear in J. Amer. Math. Soc.
7. I. Ekeland, R. Temam, Analyse Convexe et Problèmes Variationnels, Dunod Gauthier-Villars (1974).
8. L.C. Evans, Partial Differential Equations and Monge-Kantorovich Mass Transfer, Current Developments in Mathematics, forthcoming.
9. L.C. Evans, W. Gangbo, Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem, Mem. Amer. Math. Soc., Vol. 137 (1999).
10. K.J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, Cambridge (1985).
11. H. Federer, Geometric Measure Theory, Grundlehren der Math. Wiss., vol. 153, Springer-Verlag, Berlin (1969).
12. M. Feldman, R.J. McCann, Uniqueness and transport density in Monge's mass transportation problem, Calc. Var. DOI 10.1007/s005260100119.
13. I. Fragalà, C. Mantegazza, On some notion of tangent space to a measure, Proc. Roy. Soc. Edimburgh, 129A (1999), 331-342.
14. W. Gangbo, The Monge mass transfer problem and its applications, Caffarelli, Luis A. (ed.) et al., Monge Ampere equation: applications to geometry and optimization. Providence, RI: American Mathematical Society. Contemp. Math., 226, 79-104 (1999). MSC 1991
15. W. Gangbo, R.J. McCann, The geometry of optimal transportation, Acta Math., 177 (1996), 113-161.
16. U. Janfalk, On certain problems concerning the p-Laplace operator, Linkøping Studies in Science and Technology, dissertation 326, Linkøping University, Sweden, 1993.
17. A. Pratelli, Regolarità delle misure ottimali nel problema di trasporto di Monge-Kantorovich, Degree thesis, University of Pisa, Italy, 2000.
18. S.T. Rachev, L. Ruschendorf, Mass Transportation Problems, Springer-Verlag (1998).
19. L. Simon, Lectures on Geometric Measure Theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, Vol. 3 (1983).
20. V.N. Sudakov, Geometric problems in the Theory of Infinite-Dimensional Probability Distributions, Proc. of the Steklov Institue of Mathematics, 141 (1979).
21. N.S. Trudinger, X.-J. Wang, On the Monge Mass Transfer Problem, Calc. Var. 13 (2001), 19-31.