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Interfaces and Free Boundaries

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Volume 22, Issue 2, 2020, pp. 131–155
DOI: 10.4171/IFB/436

Published online: 2020-07-06

A convex approach to the Gilbert–Steiner problem

Mauro Bonafini[1] and Édouard Oudet[2]

(1) Georg-August-Universität Göttingen, Germany
(2) Université Grenoble Alpes, Grenoble, France

We describe a convex relaxation for the Gilbert–Steiner problem both in Rd and on manifolds, extending the framework proposed in [10], and we discuss its sharpness by means of calibration type arguments. The minimization of the resulting problem is then tackled numerically and we present results for an extensive set of examples. In particular we are able to address the Steiner tree problem on surfaces.

Keywords: Calculus of variations, Steiner problem, Gilbert–Steiner problem, convex relaxation, calibrations, minimal networks on surfaces

Bonafini Mauro, Oudet Édouard: A convex approach to the Gilbert–Steiner problem. Interfaces Free Bound. 22 (2020), 131-155. doi: 10.4171/IFB/436