Regularity for stationary surfaces of constant mean curvature with free boundaries
type: Item
instance of: scholarly article
title: Regularity for stationary surfaces of constant mean curvature with free boundaries
zbMATH Open document ID: 0609.49027
DOI: 10.1007/BF02399202
author: Michael Grüter
author: S. Hildebrandt
author: Johannes C. C. Nitsche
published in: Acta Mathematica
publication date: 1986-01-01T00:00:00Z
review text: The authors prove regularity for the free boundary of the partitioning problem for a convex body in \({\mathbb{R}}^ 3\) with boundary T. The body K is assumed to be partitioned into two parts \(K_ 1\) and \(K_ 2\) with given relative volumes by a \(C^ 1\)-surface S with finite stationary, for example minimal, area. It is shown that a solution S of this problem is a surface of constant mean curvature which meets the supporting surface \(T=\partial K\) orthogonally in a weak sense and that the trace is smooth. The most important step in the regularity proof is to prove the continuity of the free boundary.
Mathematics Subject Classification ID: 49Q05
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 3986047
zbMATH Keywords: regularity
zbMATH Keywords: free boundary
zbMATH Keywords: partitioning problem
zbMATH Keywords: surface of constant mean curvature
reviewed by: G. Dziuk
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3986047