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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

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Type
Article accepté pour publication ou publié
Date
2011
Journal name
Archive for Rational Mechanics and Analysis
Volume
201
Number
1
Publisher
Springer
Pages
115-142
Publication identifier
Metadata
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Author(s)
Oudet, Edouard
Santambrogio, Filippo
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 / Keywords
branched transport; Gamma-convergence; Steiner problem