Sharp summability for Monge transport density via interpolation

Luigi De Pascale; Aldo Pratelli

ESAIM: Control, Optimisation and Calculus of Variations (2004)

  • Volume: 10, Issue: 4, page 549-552
  • ISSN: 1292-8119

Abstract

top
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 ≤ + ∞ .

How to cite

top

Pascale, Luigi De, and Pratelli, Aldo. "Sharp summability for Monge transport density via interpolation." ESAIM: Control, Optimisation and Calculus of Variations 10.4 (2004): 549-552. <http://eudml.org/doc/245744>.

@article{Pascale2004,
abstract = {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\le p\le +\infty $.},
author = {Pascale, Luigi De, Pratelli, Aldo},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {transport density; interpolation; summability},
language = {eng},
number = {4},
pages = {549-552},
publisher = {EDP-Sciences},
title = {Sharp summability for Monge transport density via interpolation},
url = {http://eudml.org/doc/245744},
volume = {10},
year = {2004},
}

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
PB - EDP-Sciences
VL - 10
IS - 4
SP - 549
EP - 552
AB - 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\le p\le +\infty $.
LA - eng
KW - transport density; interpolation; summability
UR - http://eudml.org/doc/245744
ER -

References

top
  1. [1] L. Ambrosio, Mathematical Aspects of Evolving Interfaces. Lect. Notes Math. 1812 (2003) 1-52. Zbl1047.35001MR2011032
  2. [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. Zbl1065.49026MR2006307
  3. [3] G. Bouchitté and G. Buttazzo, Characterization of optimal shapes and masses through Monge-Kantorovich equation. J. Eur. Math. Soc. 3 (2001) 139-168. Zbl0982.49025MR1831873
  4. [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. Zbl0884.49023MR1451945
  5. [5] L. De Pascale, L.C. Evans and A. Pratelli, Integral Estimates for Transport Densities. Bull. London Math. Soc. 36 (2004) 383-395. Zbl1068.35170MR2038726
  6. [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. Zbl1032.49043MR1899447
  7. [7] L.C. Evans and W. Gangbo, Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem. Mem. Amer. Math. Soc. 137 (1999). Zbl0920.49004MR1464149
  8. [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. Zbl1003.49031
  9. [9] W. Gangbo and R.J. McCann, The geometry of optimal transportation. Acta Math. 177 (1996) 113-161. Zbl0887.49017MR1440931
  10. [10] M. Giaquinta, Introduction to regularity theory for nonlinear elliptic systems. Birkhäuser Verlag (1993). Zbl0786.35001MR1239172

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.