Uniform estimates for a Modica–Mortola type approximation of branched transportation
Antonin Monteil · ESAIM Control Optimisation and Calculus of Variations · 2015
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.