Published Paper

Inserted: 27 jan 2023
Last Updated: 26 apr 2026

Journal: Contemp. Math.
Volume: 809
Pages: 123-134
Year: 2025
Doi: https://doi.org/10.1090/conm/809/16205

Abstract:

We extend known existence and uniqueness results of weak measure solutions for systems of non-local continuity equations beyond the usual Lipschitz regularity. Existence of weak measure solutions holds for uniformly continuous vector fields and convolution kernels, while uniqueness follows from a Lagrangian stability estimate under an additional Osgood condition.

Keywords: Osgood condition, Non-local continuity equation, Lagrangian stability

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• Inversi, Stefani - Lagrangian stability for a system of non-local continuity equations under Osgood condition