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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/46571完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王振男 | |
| dc.contributor.author | Wen-Yen Feng | en |
| dc.contributor.author | 馮文彥 | zh_TW |
| dc.date.accessioned | 2021-06-15T05:16:16Z | - |
| dc.date.copyright | 2010-08-09 | |
| dc.date.issued | 2010 | |
| dc.date.submitted | 2010-07-21 | |
| dc.identifier.citation | [1]Alinhac, S. and Baouendi, M. S., Uniqueness for the characteristic Cauchy problem and strong unique continuation for higher order partial differential inequalities, Amer. J. Math., 102 (1980), 179--217.
[2]Aronszajn, N., Krzywcki, A. and Szarski, J., A unique continuation theorem for exterior differential forms on Riemanian manifolds, Ark. Mat., 4 (1962), 417--453. [3]Grammatico, C., Unicita forte per operatori ellittici, Tesi di Dottorato, Univ. degli Studi di Pisa (1997). [4]Ikoma, Makoto; Yamada, Osanobu Strong unique continuation property of two-dimensional Dirac equations with Aharonov-Bohm fields. (English summary) Proc. Japan Acad. Ser. A Math. Sci. 79 (2003), no. 9, 158--161. [5]Jerison, D., Carleman inequalities for the Dirac and Laplace operator and unique continuation, Adv. Math., 63 (1986), 118--134. [6]Jerison, D. and Kenig, C., Unique continuation and absence of positive eigenvalues for Schrodinger operators, Ann. of Math., 121 (1985), 463--492. [7]Kim, Yonne Mi Carleman inequalities for the Dirac operator and strong unique continuation. Proc. Amer. Math. Soc. 123 (1995), no. 7, 2103--2112. [8]Laura De Carli and Takashi Okaji, Strong Unique Continuation Property for the Dirac Equation, Publ. Res. Inst. Math. Sci., 35, 825-846(1999) [9]M.-E. Craioveanu, Mircea Puta, Themistocles M. Rassias, Mircea Craioveanu, Old and New Aspects in Spectral Geometry, Mia., 155-162(2001) [10]Niculae Mandache. Some Remarks Concerning Unique Continuation for the Dirac Operator. Letters in Mathematical Physics 3h 85-92, 1994 [11]Pan, Y. F., Unique continuation for Schrodinger operators with singular potentials, Comm. Partial Diff. Eqs., 17 (1992), 953--965. [12]T. Carleman, {it Sur un problem d'unicite les systems d'equations aux divees partielles a deux variables independentes}, Ark. Mat. Astr. Fys., 26B, (1939), 1-9. [13]Regbaoui, R., Strong unique continuation results for differential inequalities, J. Funct. Anal., 148 (1997), 508--523. [14]Regbaoui, R., Strong unique continuation for second order elliptic differential operators, J. Diff. Eqs., 141 (1997), 201--217. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/46571 | - |
| dc.description.abstract | 這篇論文是狄拉克算子強唯一連續延拓性的統整。我們知道在歐氏空間中一函數遞減至零的速度比任何多項式還要迅速，該函數仍然可能不顯然。而一微分方程或微分不等式擁有強唯一連續延拓性，指的是該微分方程或不等式的解，若於定義域上之某一點其遞減至零的速度，處處比任何多項式還要迅速，則該函數必等於零在連通的定義域上。 | zh_TW |
| dc.description.abstract | This paper is a survey of strong unique continuation property for the Dirac equation. We know that a function can be non-triviual even if it vanishes of infinite order at some point. We say a differential equation(or inequality) has strong unique continuation property(SUCP) if u is a solution of this differential equation (or inequality) and u vanishes of infinite order at some x_{0}, then u is identically zero. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T05:16:16Z (GMT). No. of bitstreams: 1 ntu-99-R97221012-1.pdf: 461287 bytes, checksum: db248e4d4436251a6b16e4b88e7911f8 (MD5) Previous issue date: 2010 | en |
| dc.description.tableofcontents | 口試委員會審定書……………………………………………………………….. i 誌謝………………………………………………………………………………... ii 中文摘要………………………………………………………………………….. iii 英文摘要………………………………………………………………………….. iv 第一章 簡介…………………………………………………………………….. 1 第二章 部份結果…………………………………………………………….. 4 第三章 定理六之證明…………………………………………………………. 11 第四章 定理七.八之證明…………………………………………………….... 25 第五章 定理九.十之證明……………………………………………………… 32 參考文獻…………………………………………………………………….…… 45 | |
| dc.language.iso | en | |
| dc.subject | 卡勒門不等式 | zh_TW |
| dc.subject | 狄拉克方程 | zh_TW |
| dc.subject | 狄拉克算子 | zh_TW |
| dc.subject | 唯一連續延拓性 | zh_TW |
| dc.subject | 強唯一連續延拓性 | zh_TW |
| dc.subject | Dirac operator | en |
| dc.subject | Carleman-type inequalities | en |
| dc.subject | Strong unique continuation property | en |
| dc.subject | unique continuation property | en |
| dc.subject | Dirac equation | en |
| dc.title | 狄拉克算子強唯一連續延拓性的統整 | zh_TW |
| dc.title | The strong unique continuation property for the Dirac operator | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 98-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳俊全,林景隆 | |
| dc.subject.keyword | 狄拉克方程,狄拉克算子,唯一連續延拓性,強唯一連續延拓性,卡勒門不等式, | zh_TW |
| dc.subject.keyword | Dirac operator,Dirac equation,unique continuation property,Strong unique continuation property,Carleman-type inequalities, | en |
| dc.relation.page | 46 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2010-07-22 | |
| 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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