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 1≤p≤+∞.

DOI : 10.1051/cocv:2004019
Classification : 41A05, 49N60, 49Q20, 90B06
Mots-clés : transport density, interpolation, summability 
@article{COCV_2004__10_4_549_0,
     author = {Pascale, Luigi De and Pratelli, Aldo},
     title = {Sharp summability for {Monge} transport density via interpolation},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {549--552},
     publisher = {EDP-Sciences},
     volume = {10},
     number = {4},
     year = {2004},
     doi = {10.1051/cocv:2004019},
     mrnumber = {2111079},
     zbl = {1072.49033},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv:2004019/}
}
TY  - JOUR
AU  - Pascale, Luigi De
AU  - Pratelli, Aldo
TI  - Sharp summability for Monge transport density via interpolation
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2004
SP  - 549
EP  - 552
VL  - 10
IS  - 4
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/cocv:2004019/
DO  - 10.1051/cocv:2004019
LA  - en
ID  - COCV_2004__10_4_549_0
ER  - 
%0 Journal Article
%A Pascale, Luigi De
%A Pratelli, Aldo
%T Sharp summability for Monge transport density via interpolation
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2004
%P 549-552
%V 10
%N 4
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/cocv:2004019/
%R 10.1051/cocv:2004019
%G en
%F COCV_2004__10_4_549_0
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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

[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

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

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

Cité par Sources :