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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/41163完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳金次 | |
| dc.contributor.author | Bing-Kun Tsai | en |
| dc.contributor.author | 蔡秉昆 | zh_TW |
| dc.date.accessioned | 2021-06-14T17:20:57Z | - |
| dc.date.available | 2018-07-24 | |
| dc.date.copyright | 2008-08-05 | |
| dc.date.issued | 2008 | |
| dc.date.submitted | 2008-07-24 | |
| dc.identifier.citation | References
[1] J-T Chen and W-S Huang, Convexity of capillary surfaces in the outer space, Invent. Math. 67(1982), p.253-259. [2] R. Courant and D. Hilber, Methods of mathematical physics, Vol.II, Inter-science, New York, 1962. [3] R. Finn, A subsidiary variational problem and existence criteria for capillary surfaces, J. Reine Angew. Math. 353(1984), p.196-214. [4] R. Finn, Equilibrium capillary surfaces, Grundlehren Math. Wiss. Vol. 284, Springer-Verlag, New York, 1986. [5] R. Finn and J-F Hwang, On the comparison principle for capillary surfaces, J. Fac. Sci. Univ. Tokyo Sect. IA. Math. 36(1989) No.1 p131-134. [6] E. Giusti, Generalized solutions of mean curvature equations, Pacific J. Math. 88(1980), p.297-321. [7] J-F Hwang, Comparison principle and Liouville theorems for prescribed mean curvature equations in unbounded domains, Annali Scuola Norm. Sup. Pisa. IV15(1988) p.341-355. [8] J-f Hwang, How many theorems can be derived from a vector function - on uniqueness theorems for the minimal surface equation, Taiwanese J. Math. Vol.7(2003), No. 4, pp.513-539. [9] C-C Lee, A uniqueness theorem for the minimal surface equation on an un-bounded domain in R2 Pacific J. Math. 177(1977), No.1 p103-107. [10] U. Massari, Frontere orientate di curvature media assegnata in Lp, Rend. Sem. Tat. Univ. Padova 53(1975), p.37-52. [11] M. Miranda, superfici minime illimitate, Ann. Scuola Norm. Sup. Pisa. (4) 4(1977), p.313-322 [12] J. C. C. Nitsche, On new resulls in the theory of minimal surfaces, Bull. Amer. Math. Soc. 71(1965), p.195-270. [13] R. Osserman, Asurvey of minimal surfaces, Ven Nostrand-Reinhold. New York, 1969. [14] L. F. Tam, On the uniqueness of capillary surfaces without gravity over an infinte strip, Indana Univ. Math. J. 36(1987) p.79-89. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/41163 | - |
| dc.description.abstract | 我們考慮在無界扇形域上，給定邊界接觸角的最小曲面方程式。首先，我們對於方程式線性解的存在性，給出一個充要條件。其次，透過「吹」及「吸」兩種過程，我們研究方程式解在原點及無窮遠處的行為。最後，我們論述方程式解在邊界上是線性的，同時證明解是一個平面。 | zh_TW |
| dc.description.abstract | We consider the minimal surface equation in an infinite sector domain with given capillary boundary conditions.First, we give a necessary and sufficient conditions for the existence of the linear solution. Second, we study the behavior of the solutions of the minimal surface equation at the origin and at the infinite by using the blow up and the sip in process. Finally, we claim that the solution is linear on the boundary and conclude that it is a plane. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-14T17:20:57Z (GMT). No. of bitstreams: 1 ntu-97-R95221006-1.pdf: 213023 bytes, checksum: b5746c5e02e5ed59132384b4bc29cac2 (MD5) Previous issue date: 2008 | en |
| dc.description.tableofcontents | Contents
口試委員會審定書 i Abstract in Chinese ii Abstract in English iii 1 Introduction 1 2 The Necessary and Sufficient Conditions for the Existence of a Linear Solution 3 3 The Behavior of u at the Origin and the Infinity. 4 4 The Behavior of u on the Boundary 7 5 u is linear 11 References 12 | |
| dc.language.iso | en | |
| dc.subject | 最小曲面 | zh_TW |
| dc.subject | 偏微分方程 | zh_TW |
| dc.subject | 邊界接觸角 | zh_TW |
| dc.subject | 扇形域 | zh_TW |
| dc.subject | 無界域 | zh_TW |
| dc.subject | unbound domain | en |
| dc.subject | PDE | en |
| dc.subject | minimal surface | en |
| dc.subject | capillary boundary condition | en |
| dc.subject | sector domain | en |
| dc.title | 邊界接觸角給定下最小曲面在無界扇形域上的唯一定理 | zh_TW |
| dc.title | On the Uniqueness of Minimal Surface Equation in an Infinite Sector Domain
with Capillary Boundary Condition | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 96-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 王藹農,黃振芳 | |
| dc.subject.keyword | 最小曲面,無界域,扇形域,邊界接觸角,偏微分方程, | zh_TW |
| dc.subject.keyword | minimal surface,unbound domain,sector domain,capillary boundary condition,PDE, | en |
| dc.relation.page | 13 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2008-07-26 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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