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arXiv · 1311.1392

On sets minimizing their weighted length in uniformly convex separable Banach spaces

De Pauw Thierry·Lemenant Antoine·Millot Vincent
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Abstract

We study existence and partial regularity relative to the weighted Steiner problem in Banach spaces. We show $C^1$ regularity almost everywhere for almost minimizing sets in uniformly rotund Banach spaces whose modulus of uniform convexity verifies a Dini growth condition.

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De Pauw Thierry, Lemenant Antoine, Millot Vincent. 2013-11-02. On sets minimizing their weighted length in uniformly convex separable Banach spaces. https://arxiv.org/abs/1311.1392

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