Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-29T03:23:20.968Z Has data issue: false hasContentIssue false
  • English
  • Français

Sharp summability for Monge Transport densityvia Interpolation

Published online by Cambridge University Press:  15 October 2004

Luigi De Pascale  and
Aldo Pratelli
Luigi De Pascale
Affiliation:
Dipartimento di Matematica Applicata, Università di Pisa, via Bonanno Pisano 25/B, 56126 Pisa, Italy; [email protected].
Aldo Pratelli
Affiliation:
Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy; [email protected].
Get access

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 $1\leq p\leq +\infty$ .

Keywords

Transport densityinterpolationsummability.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 4 , October 2004 , pp. 549 - 552
Copyright
© EDP Sciences, SMAI, 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ambrosio, L., Mathematical Aspects of Evolving Interfaces. Lect. Notes Math. 1812 (2003) 1-52. CrossRef
Ambrosio, L. and Pratelli, A., Existence and stability results in the L 1 theory of optimal transportation. Lect. Notes Math. 1813 (2003) 123-160. CrossRef
Bouchitté, G. and Buttazzo, G., Characterization of optimal shapes and masses through Monge-Kantorovich equation. J. Eur. Math. Soc. 3 (2001) 139-168.
Bouchitté, G., Buttazzo, G. and Seppecher, P., Shape Optimization Solutions via Monge-Kantorovich Equation. C. R. Acad. Sci. Paris I 324 (1997) 1185-1191. CrossRef
De Pascale, L., Evans, L.C. and Pratelli, A., Integral Estimates for Transport Densities. Bull. London Math. Soc. 36 (2004) 383-395. CrossRef
De Pascale, L. and Pratelli, A., Regularity properties for Monge transport density and for solutions of some shape optimization problem. Calc. Var. Partial Differ. Equ. 14 (2002) 249-274. CrossRef
L.C. Evans and W. Gangbo, Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem. Mem. Amer. Math. Soc. 137 (1999).
Feldman, M. and McCann, R., Uniqueness and transport density in Monge's mass transportation problem. Calc. Var. Partial Differ. Equ. 15 (2002) 81-113. CrossRef
Gangbo, W. and McCann, R.J., The geometry of optimal transportation. Acta Math. 177 (1996) 113-161. CrossRef
M. Giaquinta, Introduction to regularity theory for nonlinear elliptic systems. Birkhäuser Verlag (1993).