Accepted Paper

Inserted: 10 nov 2009
Last Updated: 11 may 2010

Journal: J. Math. Pures Appl.
Year: 2009

Abstract:

In this paper we introduce a new transportation distance between non-negative measures inside a domain $\O$. This distance enjoys many nice properties, for instance it makes the space of non-negative measures inside $\O$ a geodesic space without any convexity assumption on the domain. Moreover we will show that the gradient flow of the entropy functional $\int_\O [\rho \log(\rho) - \rho]\,dx$ with respect to this distance coincides with the heat equation, subject to the Dirichlet boundary condition equal to $1$.

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• DirichletW2.pdf