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


Submitted Paper

Inserted: 27 jan 2023
Last Updated: 27 jan 2023

Year: 2023


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