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 $Omega$. Moreover, we will show that the gradient flow of the entropy functional w.r.t. this distance coincides with the heat equation, subject to the Dirichlet boundary condition equal to 1

A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions / Figalli, A.; Gigli, N.. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 94:2(2010), pp. 107-130. [10.1016/j.matpur.2009.11.005]

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

Gigli, N.
2010-01-01

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 $Omega$. Moreover, we will show that the gradient flow of the entropy functional w.r.t. this distance coincides with the heat equation, subject to the Dirichlet boundary condition equal to 1
2010
94
2
107
130
https://doi.org/10.1016/j.matpur.2009.11.005
Figalli, A.; Gigli, N.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/16162
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