Uniform estimates for a Modica–Mortola type approximation of branched transportation
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 1, pp. 309-335.

Models for branched networks are often expressed as the minimization of an energy M α over vector measures concentrated on 1-dimensional rectifiable sets with a divergence constraint. We study a Modica–Mortola type approximation M α ε , introduced by Edouard Oudet and Filippo Santambrogio, which is defined over H 1 vector measures. These energies induce some pseudo-distances between L 2 functions obtained through the minimization problem min{M α ε (u): ·u=f + -f - }. We prove some uniform estimates on these pseudo-distances which allow us to establish a Γ-convergence result for these energies with a divergence constraint.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2015049
Classification : 49J45, 90B06, 90B18
Mots clés : Branched transportation networks, Γ-convergence, phase field models
Monteil, Antonin 1

1 Laboratoire de Mathématiques d’Orsay, Université Paris-Sud 11, Bât. 425, 91405 Orsay, France.
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Monteil, Antonin. Uniform estimates for a Modica–Mortola type approximation of branched transportation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 1, pp. 309-335. doi : 10.1051/cocv/2015049. http://www.numdam.org/articles/10.1051/cocv/2015049/

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