Calculus of Variations and Geometric Measure Theory

E. Oudet - F. Santambrogio

A Modica-Mortola approximation for branched transport and applications

created by santambro on 13 Jan 2011


Accepted Paper

Inserted: 13 jan 2011

Journal: Arch. Rati. Mech. An.
Year: 2011

This paper is the new updated version, including numerical simulations, of the previous preprint already present on this website, which was finally turned into a CRAS note.


The $M^\alpha$ energy which is usually minimized in branched transport problems among singular 1-dimensional recti able vector measures is approximated by means of a sequence of elliptic energies de ned on more regular vector fi elds. 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 convergence and numerical simulations of optimal networks based on that previous result.

Keywords: Gamma-convergence, Branched transport, Steiner problem