On the connectivity of boundaries of sets minimizing perimeter subject to a volume constraint
type: Item
instance of: scholarly article
title: On the connectivity of boundaries of sets minimizing perimeter subject to a volume constraint
zbMATH Open document ID: 0930.49024
author: Peter Sternberg
author: Kevin Zumbrun
published in: Communications in Analysis and Geometry
publication date: 2000-02-06T00:00:00Z
review text: The authors study the problem of locally minimizing perimeter within a given bounded domain \(\Omega\) in \textbf{R}\(^n\) subject to a volume constraint. The main result of the paper asserts that if \(\Omega\) is convex then the boundary of any local minimizer is connected. Several interesting applications in the theory of isoperimetric inequalities or in variational problems related to phase transitions are given.
Mathematics Subject Classification ID: 49Q20
Mathematics Subject Classification ID: 58E15
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 1295158
zbMATH Keywords: minimization problem
zbMATH Keywords: connected set
zbMATH Keywords: mean curvature
zbMATH Keywords: isoperimetric inequalities
reviewed by: Vicenţiu D. Rădulescu
MaRDI profile type: Publication
DOI: 10.4310/CAG.1999.V7.N1.A7
description: scientific article; zbMATH DE number 1295158