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

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• 作者：Thierry De Pauw ; ^{thierry.de-pauw@imj-prg.fr" class="auth_mail" title="E-mail the corresponding author} ; Antoine Lemenant ^{lemenant@ljll.univ-paris-diderot.fr" class="auth_mail" title="E-mail the corresponding author} ; Vincent Millot ^{millot@ljll.univ-paris-diderot.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Steiner problem ; Geometric measure theory
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：10 January 2017
• 年：2017
• 卷：305
• 期：Complete
• 页码：1268-1319
• 全文大小：784 K

文摘

We study existence and partial regularity relative to the weighted Steiner problem in Banach spaces. We show C¹$C^1$ regularity almost everywhere for almost minimizing sets in uniformly rotund Banach spaces whose modulus of uniform convexity verifies a Dini growth condition.