A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions

作者：Figalli Alessio^*; Gigli Nicola

来源：Journal de Mathematiques Pures et Appliquees, 2010, 94(2): 107-130.

DOI：10.1016/j.matpur.2009.11.005

• Transportation distances
• Gradient flows
• Heat equation
• Dirichlet boundary conditions

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 integral(Omega)vertical bar rho log(rho) - rho vertical bar dx with respect to this distance coincides with the heat equation, subject to the Dirichlet boundary condition equal to 1. Published by Elsevier Masson SAS.

• 出版日期2010-8