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Uniqueness of signed measures solving the continuity equation for Osgood vector fields

Bernard, Patrick; Ambrosio, Luigi (2008), Uniqueness of signed measures solving the continuity equation for Osgood vector fields, Atti della Accademia Nazionale dei Lincei. Classe di scienze fisiche, matematiche e naturali, Matematica e applicazioni, 19, 3, p. 237--245

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00294648/en/
Date
2008
Journal name
Atti della Accademia Nazionale dei Lincei. Classe di scienze fisiche, matematiche e naturali, Matematica e applicazioni
Volume
19
Number
3
Pages
237--245
Metadata
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Author(s)
Bernard, Patrick cc
Ambrosio, Luigi
Abstract (EN)
Nonnegative measure-valued solutions of the continuity equation are uniquely determined by their initial condition, if the characteristic ODE associated to the velocity field has a unique solution. In this paper we give a partial extension of this result to signed measure-valued solutions, under a quantitative two-sided Osgood condition on the velocity field. Our results extend those obtained for log-Lipschitz vector fields by Bahouri and Chemin.
Subjects / Keywords
Analysis of PDEs; Dynamical Systems