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math.AP2013★ 1 cited
A Modica-Mortola approximation for the Steiner Problem
Antoine Lemenant, Filippo Santambrogio
In this note we present a way to approximate the Steiner problem by a family of elliptic energies of Modica-Mortola type, with an additional term relying on the weighted geodesic d…
math.FA2013
On sets minimizing their weighted length in uniformly convex separable Banach spaces
De Pauw Thierry, Lemenant Antoine, Millot Vincent
We study existence and partial regularity relative to the weighted Steiner problem in Banach spaces. We show regularity almost everywhere for almost minimizing sets in unifor…