A Modica-Mortola Approximation for Branched Transport and Applications

The M ^α energy which is usually minimized in branched transport problems among singular one-dimensional rectifiable vector measures is approximated by means of a sequence of elliptic energies defined on more regular vector fields. The procedure recalls the one of Modica-Mortola related to the approximation of the perimeter. In our context, the double-well potential is replaced by a concave term. The paper contains a proof of Γ−convergence and numerical simulations of optimal networks based on that previous result.