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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].
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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

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