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 ≤ +∞.
Sharp summability for Monge Transport density via Interpolation
DE PASCALE, LUIGI;PRATELLI, A.
2004-01-01
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 ≤ p ≤ +∞.File in questo prodotto:
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