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研究生： 凌家東
Chia-Tung Ling
論文名稱：
On The Equilibrium Positions of A Square On An Elastic Wire with Energy Involving Arc Length
指導教授： 郭忠勝
Guo, Jong-Shenq
學位類別： 碩士
Master
系所名稱： 數學系
Department of Mathematics
論文出版年： 2003
畢業學年度： 91
語文別： 中文
論文頁數： 33
英文關鍵詞： The Equilibrium Positions of A Square, An Elastic Wire, Energy Involving Arc Length
論文種類： 學術論文
相關次數： 點閱：103  下載：10 
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    • We study the equilibrium positions of a square, allowing to move
    freely on an elastic wire. The energy under consideration is involving
    the arc length of admissible function. We obtain the necessary and
    sufficient condition for the existence of minimizers on the weight of
    the solid body in each case. We also characterize the position(s) of the
    minimizer(s) in each case.

    1. Introduction………………………………………………1 2. Preliminary……………………………………………… 3 3. Existence of a minimizer of (1.4) …………………7 4. Computation of the minimizers………………………19 References……………………………………………………28 Appendix………………………………………………………29

    [1] A. Aissani, M. Chipot, On the equilibrium position of a square on an elastic wire,
    J. Conv. Anal. 8 (2001), 171-195.
    [2] A. Aissani, M. Chipot, S.Fouad, On the deformation of an elastic wire by one or
    two heavy disks, Arch. Math. 76 (2001), 467-480.
    [3] J. Bemelmans, M. Chipot, On a variational problem for an elastic membrane supporting
    a heavy ball, Calc. Var. 3 (1995), 447-473.
    [4] M. Chipot, Elements of Nonlinear Analysis, Birkh¨auser, 2000.
    [5] D. Kinderlehrer, G. Stampacchia, An introduction to Variational Inequalities and
    Their Applications, Academic. Press, 1980.
    [6] J.F. Rodrigues, Obstacle Problems in Mathematical Physics, North Holland Studies
    134, Amsterdam, North Holland, 1987.
    [7] A. Wouk, A Course of Applied Functional Analysis, Wiley, 1979.

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