A Modica-Mortola Approximation for Branched Transport and Applications
Oudet, Edouard; Santambrogio, Filippo (2011), A Modica-Mortola Approximation for Branched Transport and Applications, Archive for Rational Mechanics and Analysis, 201, 1, p. 115-142. http://dx.doi.org/10.1007/s00205-011-0402-6
TypeArticle accepté pour publication ou publié
Journal nameArchive for Rational Mechanics and Analysis
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Abstract (EN)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.
Subjects / Keywordsbranched transport; Gamma-convergence; Steiner problem
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