Some aspects of the variational nature of mean curvature flow
type: Item
instance of: scholarly article
title: Some aspects of the variational nature of mean curvature flow
zbMATH Open document ID: 1155.49007
DOI: 10.4171/JEMS/138
author: Luca Mugnai
author: Giovanni Bellettini
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2008-11-12T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: The authors consider, in the first part of the paper, a second order space-time functional for which the solutions of the classical heat equation are minimizers. This point of view is the starting point for the study of a more difficult situation as the mean curvature flow of an embedded hypersurface in \(\mathbb R^n\). In particular the authors define an appropriate functional as the sum of two competing terms: the first depending on the normal \(\nu\) (singular in the part where \(\nu_{n+1}= 1\)) and the other, of second order, which is the Willmore functional of the time slice of the hypersurface integrated further in time. For the proposed functional the authors, with an appropriate definition of mean curvature flow, study, in a very extensive way, lower semicontinuity, coercivity, minimum problem and give, also, some results on approximation in the framework of the \(\Gamma\)-convergenge theory.
reviewed by: Eduardo Pascali
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 35K10
zbMATH DE Number: 5365143
zbMATH Keywords: heat equation
zbMATH Keywords: space-time energy minimizers
zbMATH Keywords: mean curvature flow
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5365143