Volume 10, Number 4, October 2004
|Page(s)||549 - 552|
|Published online||15 October 2004|
Sharp summability for Monge Transport density via Interpolation
Dipartimento di Matematica Applicata, Università di Pisa,
via Bonanno Pisano 25/B, 56126 Pisa, Italy; firstname.lastname@example.org.
2 Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy; email@example.com.
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 .
Mathematics Subject Classification: 41A05 / 49N60 / 49Q20 / 90B06
Key words: Transport density / interpolation / summability.
© EDP Sciences, SMAI, 2004
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