Sharp summability for Monge transport density via interpolation
ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 4, pp. 549-552.

Using some results proved in De Pascale and Pratelli [Calc. Var. Partial Differ. Equ. 14 (2002) 249-274] (and De Pascale et al. [Bull. London Math. Soc. 36 (2004) 383-395]) and a suitable interpolation technique, we show that the transport density relative to an L p source is also an L p function for any 1p+.

DOI : https://doi.org/10.1051/cocv:2004019
Classification : 41A05,  49N60,  49Q20,  90B06
Mots clés : transport density, interpolation, summability
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     title = {Sharp summability for {Monge} transport density via interpolation},
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Pascale, Luigi De; Pratelli, Aldo. Sharp summability for Monge transport density via interpolation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 4, pp. 549-552. doi : 10.1051/cocv:2004019. http://www.numdam.org/articles/10.1051/cocv:2004019/

[1] L. Ambrosio, Mathematical Aspects of Evolving Interfaces. Lect. Notes Math. 1812 (2003) 1-52. | MR 2011032 | Zbl 1047.35001

[2] L. Ambrosio and A. Pratelli, Existence and stability results in the L 1 theory of optimal transportation. Lect. Notes Math. 1813 (2003) 123-160. | MR 2006307 | Zbl 1065.49026

[3] G. Bouchitté and G. Buttazzo, Characterization of optimal shapes and masses through Monge-Kantorovich equation. J. Eur. Math. Soc. 3 (2001) 139-168. | MR 1831873 | Zbl 0982.49025

[4] G. Bouchitté, G. Buttazzo and P. Seppecher, Shape Optimization Solutions via Monge-Kantorovich Equation. C. R. Acad. Sci. Paris I 324 (1997) 1185-1191. | MR 1451945 | Zbl 0884.49023

[5] L. De Pascale, L.C. Evans and A. Pratelli, Integral Estimates for Transport Densities. Bull. London Math. Soc. 36 (2004) 383-395. | MR 2038726 | Zbl 1068.35170

[6] L. De Pascale and A. Pratelli, Regularity properties for Monge transport density and for solutions of some shape optimization problem. Calc. Var. Partial Differ. Equ. 14 (2002) 249-274. | MR 1899447 | Zbl 1032.49043

[7] L.C. Evans and W. Gangbo, Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem. Mem. Amer. Math. Soc. 137 (1999). | MR 1464149 | Zbl 0920.49004

[8] M. Feldman and R. Mccann, Uniqueness and transport density in Monge's mass transportation problem. Calc. Var. Partial Differ. Equ. 15 (2002) 81-113. | Zbl 1003.49031

[9] W. Gangbo and R.J. Mccann, The geometry of optimal transportation. Acta Math. 177 (1996) 113-161. | MR 1440931 | Zbl 0887.49017

[10] M. Giaquinta, Introduction to regularity theory for nonlinear elliptic systems. Birkhäuser Verlag (1993). | MR 1239172 | Zbl 0786.35001

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