Published Paper

Inserted: 10 nov 2009
Last Updated: 9 aug 2024

Journal: J. Math. Pures Appl.
Year: 2010

Abstract:

In this paper, we introduce a new transportation distance between non-negative measures inside a domain \(\Omega\). This distance enjoys many nice properties; for instance, it makes the space of non-negative measures inside \(\Omega\) a geodesic space without any convexity assumption on the domain. Moreover, we will show that the gradient flow of the entropy functional

\[ \int_{\Omega} \left[\rho \log(\rho) - \rho\right] \, dx \]

with respect to this distance coincides with the heat equation, subject to the Dirichlet boundary condition equal to 1.

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