Accepted Paper

Inserted: 13 jan 2011

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

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.

Abstract:

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

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• irrigation_v5.pdf