Calculus of Variations and Geometric Measure Theory

M. Inversi - G. Stefani

Lagrangian stability for a system of non-local continuity equations under Osgood condition

created by stefani on 27 Jan 2023
modified on 09 Aug 2023


Accepted Paper

Inserted: 27 jan 2023
Last Updated: 9 aug 2023

Journal: Contemp. Math.
Year: 2023

ArXiv: 2301.11822 PDF


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