The variational problem for a certain space-time functional defined on planar closed curves

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• 作者：Shinya Okabe ^{okabe@math.tohoku.ac.jp}
• 关键词：53C44 ; 34B15 ; 35A15 ; 35G20 ; 49J45 ; 58E10
• 刊名：Journal of Differential Equations
• 出版年：2012
• 期刊代码：74_00220396
• 类别：mt
• 出版时间：15 May, 2012
• 卷：252
• 期：10
• 页码：5155-5184
• 文件大小：314 K

摘要

We consider a variational problem for a certain space-time functional defined on planar closed curves. The functional is related to the functional appeared in Bellettini and Mugnai (2008) . The variational problem is stated as follows: 鈥淟et and denote planar closed curves and T be a positive constant. Minimize the space-time functional over family of planar closed curves, which change from at time into at time 鈥? Concerning the variational problem, we prove the existence of minimizer in a radially symmetric class and determine all the minimizers for each initial final data. Moreover we show that there exists a unique non-radially symmetric critical point in a neighborhood of a certain radially symmetric minimizer.