Sharp summability for Monge Transport density via Interpolation

Luigi De Pascale; Aldo Pratelli

ESAIM: Control, Optimisation and Calculus of Variations (2010)

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

Abstract

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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 Lp source is also an Lp function for any 1 p + .

How to cite

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De Pascale, Luigi, and Pratelli, Aldo. "Sharp summability for Monge Transport density via Interpolation." ESAIM: Control, Optimisation and Calculus of Variations 10.4 (2010): 549-552. <http://eudml.org/doc/90742>.

@article{DePascale2010,
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 Lp source is also an Lp function for any $1\leq p\leq +\infty$. },
author = {De Pascale, Luigi, Pratelli, Aldo},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Transport density; interpolation; summability.; transport density; summability},
language = {eng},
month = {3},
number = {4},
pages = {549-552},
publisher = {EDP Sciences},
title = {Sharp summability for Monge Transport density via Interpolation},
url = {http://eudml.org/doc/90742},
volume = {10},
year = {2010},
}

TY - JOUR
AU - De Pascale, Luigi
AU - Pratelli, Aldo
TI - Sharp summability for Monge Transport density via Interpolation
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
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 Lp source is also an Lp function for any $1\leq p\leq +\infty$.
LA - eng
KW - Transport density; interpolation; summability.; transport density; summability
UR - http://eudml.org/doc/90742
ER -

References

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  1. L. Ambrosio, Mathematical Aspects of Evolving Interfaces. Lect. Notes Math.1812 (2003) 1-52.  
  2. L. Ambrosio and A. Pratelli, Existence and stability results in the L1 theory of optimal transportation. Lect. Notes Math.1813 (2003) 123-160.  Zbl1065.49026
  3. G. Bouchitté and G. Buttazzo, Characterization of optimal shapes and masses through Monge-Kantorovich equation. J. Eur. Math. Soc.3 (2001) 139-168.  Zbl0982.49025
  4. G. Bouchitté, G. Buttazzo and P. Seppecher, Shape Optimization Solutions via Monge-Kantorovich Equation. C. R. Acad. Sci. Paris I324 (1997) 1185-1191.  Zbl0884.49023
  5. L. De Pascale, L.C. Evans and A. Pratelli, Integral Estimates for Transport Densities. Bull. London Math. Soc.36 (2004) 383-395.  Zbl1068.35170
  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.  Zbl1032.49043
  7. L.C. Evans and W. Gangbo, Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem. Mem. Amer. Math. Soc.137 (1999).  Zbl0920.49004
  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.  Zbl1003.49031
  9. W. Gangbo and R.J. McCann, The geometry of optimal transportation. Acta Math.177 (1996) 113-161.  Zbl0887.49017
  10. M. Giaquinta, Introduction to regularity theory for nonlinear elliptic systems. Birkhäuser Verlag (1993).  Zbl0786.35001

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