A Modica-Mortola approximation for branched transport

Filippo Santambrogio

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arXiv · 0909.2930

A Modica-Mortola approximation for branched transport

Filippo Santambrogio

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Abstract

The M^αenergy which is usually minimized in branched transport problems among singular 1-dimensional rectifiable vector measures with prescribed divergence is approximated (and convergence is proved) by means of a sequence of elliptic energies, defined on more regular vector fields. The procedure recalls the Modica-Mortola one for approximating the perimeter, and the double-well potential is replaced by a concave power.

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Filippo Santambrogio. 2009-09-16. A Modica-Mortola approximation for branched transport. https://arxiv.org/abs/0909.2930

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