We introduce an optimal transportation interpretation of the Kantorovich norm on the space of signed Radon measures with finite mass, based on the generalized Wasserstein distance for measures with different masses. With this new interpretation, we obtain new topological properties for this norm. We use these tools to prove existence and uniqueness for solutions to non-local transport equations with source terms, when the initial condition is a signed measure.
A Wasserstein norm for signed measures, with application to non-local transport equation with source term
Rossi, Francesco;
2023-01-01
Abstract
We introduce an optimal transportation interpretation of the Kantorovich norm on the space of signed Radon measures with finite mass, based on the generalized Wasserstein distance for measures with different masses. With this new interpretation, we obtain new topological properties for this norm. We use these tools to prove existence and uniqueness for solutions to non-local transport equations with source terms, when the initial condition is a signed measure.
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