Calculus of Variations and Geometric Measure Theory
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X. Y. Lu

Branching time estimates in quasi-static evolution for the average distance functional

created by lu on 21 Feb 2011
modified on 13 Nov 2012


Published Paper

Inserted: 21 feb 2011
Last Updated: 13 nov 2012

Journal: Commun. Appl. Anal.
Volume: 16
Number: 2
Pages: 229-248
Year: 2011


In this paper we consider the quasi-static irreversible evolution of a connected network related to an average distance functional minimization problem. Our main goal is to determine whether new branches may appear during the evolution, thus changing the topology. We would give conditions on this, and an upper bound for the time at which it happens. We will use extensively tools belonging to minimizing movements and optimal transportation theory with free Dirichlet regions. Then we will give some explicit examples of quasi-static evolution, whose branching time will be estimated by direct computation, showing that the branching behavior is quite unrelated to topological proprieties.

Keywords: Optimal transport, minimizing movements, Euler scheme, average distance


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