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, Aldo;. - In: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. - ISSN 1262-3377. - STAMPA. - 10:4(2004), pp. 549-552. [10.1051/cocv:2004019]
Sharp summability for Monge Transport density via Interpolation
DE PASCALE, LUIGI;
2004
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 ≤ +∞.
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