UNIFORM ESTIMATES FOR A MODICA-MORTOLA TYPE APPROXIMATION OF BRANCHED TRANSPORTATION

作者：Monteil Antonin^*

来源：ESAIM: Control, Optimisation and Calculus of Variations , 2017, 23(1): 309-335.

DOI：10.1051/cocv/2015049

• Branched transportation networks
• Gamma-convergence
• phase field models

Models for branched networks are often expressed as the minimization of an energy M-alpha over vector measures concentrated on 1-dimensional rectifiable sets with a divergence constraint. We study a Modica-Mortola type approximation M-epsilon(alpha), 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-epsilon(alpha)(u): del center dot u = f(+) - f(-)}. We prove some uniform estimates on these pseudo-distances which allow us to establish a Gamma-convergence result for these energies with a divergence constraint.

• 出版日期2017-3