Calculus of Variations and Geometric Measure Theory

M. Bonafini - E. Oudet

A convex approach to the Gilbert-Steiner problem

created by bonafini on 12 Oct 2018
modified on 20 Jun 2021


Published Paper

Inserted: 12 oct 2018
Last Updated: 20 jun 2021

Journal: Interfaces and Free Boundaries
Volume: 22
Number: 2
Pages: 131-155
Year: 2020
Doi: 10.4171/IFB/436


We describe a convex relaxation for the Gilbert-Steiner problem both in $R^d$ and on manifolds, extending the framework proposed in 9, 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: convex relaxation, Gilbert-Steiner problem, Steiner tree problem on surfaces