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arXiv · 0807.1592

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

Luigi Ambrosio·Patrick Bernard
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Abstract

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.

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Luigi Ambrosio, Patrick Bernard. 2008-07-10. Uniqueness of signed measures solving the continuity equation for Osgood vector fields. https://arxiv.org/abs/0807.1592

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