Inserted: 13 jan 2011
Journal: Arch. Rati. Mech. An.
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 rectiable vector measures is approximated by means of a sequence of elliptic energies dened 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 convergence and numerical simulations of optimal networks based on that previous result.
Keywords: Gamma-convergence, Branched transport, Steiner problem