Publications-Theses
Article View/Open
Publication Export
Google ScholarTM
NCCU Library
Citation Infomation
Related Publications in TAIR
| Title | 殼域上的 -方程解與均勻估計 |
| Creator | 謝佩玲 Peiling Hsieh |
| Contributor | 陳天進 Ten-ging Chen 謝佩玲 Peiling Hsieh |
| Key Words | 均勻估計 |
| Date | 2002 |
| Date Issued | 17-Sep-2009 13:44:46 (UTC+8) |
| Summary | 在這篇論文裡，我們將用Henkin的積分表現法寫出***u=f在C^n上的球域與殼域的解。 除此之外，我們將估計常數C以滿足***-方程的均勻估計，即||u||∞≦C||f||∞。 In this thesis, we will write down the Henkin`s solutions of ***u=f for arbitrary ***-closed (0,1)-form f on the open balls and shell domains in C^n, and then proceed to find an explicit upper bound C such that the uniform estimates hold in these domains; that is, ||u||∞≦C||f||∞. |
| 參考文獻 | [1] T. G. Chen, On Henkin`s solution of the ***-problem on strictly convex domains in C^n, Universtity of California at Berkeley Ph. D. Thesis, 1985. [2] T. G. Chen, Geometry of strictly convex domains and an application to the uniform estimate of the ***-problem, Trans. Amer. Math. Soc. 347, (1995), 2127-2137. [3] T. G. Chen and L. J. Lin, Integral representation of solution for ***u=f and its uniform estimate on ellipsoids, Soochow Journal of Mathematics 21, (1995), 313-334. [4] H. Grauert and I. Lieb, Das Ramirezsche Integral und die Losung der Gleichung im Bereich der beschrankten Formen, Rice Univ. Studies 56(1970) no. 2, 29-50. [5] G. M. Henkin, Integral representations of functions holomorphic in strictly pseudoconvex domains and applications to the ***-problem, Mat. Sb. 82(124), 300-308 (1979); Math. U.S.S.R. Sb. 11(1970), 273-281. [6] G. M. Henkin and J. Leuterer, Theory of functions on complex manifolds, Birkfauser, Boston, Mass., 1984. [7] L. Hormander, L^2 estimates and existence theorems for the *** operator, Acta Math., 113(1965), 82-152. [8] L. Hormander, Introduction to complex analysis in several variables, North Holland, Amsterdam, 1973. [9] N. Kerzman, Holder and L^p estimates for solution of ***u=f on strongly pseudoconvex domains, Comm. Pure. Appl. Math., XXIV(1971), 301-380. [10]S. G. Krantz, Function theory of several complex variables, 2nd ed. Wadsworth and Brooks, pacific Grove, CA. [11]S. Long, Comples analysis, Reading, Mass., Addison-Wesley Pub. Co., 1977. [12]E. Ramirez, Divisions problem in der komplexen analysis mit einer Anwendung auf Rand integral darstellung, Math. Ann., 184(1970), 172-187. [13]R. M. Range, Holomorphic functions and integral representations in several complex variables, Springer- Verlag New York Inc., 1986. [14]H. Shi, Uniform estimates for the ***-equation on balls, Proc. of the 1980 Beijing Symp. on differential geometry and differential equations, Science Press, Beihing, China, 1982, Gordon and Breach, Science Publisher, Inc., New York, vol. 3, 1431-1439. |
| Description | 碩士 國立政治大學 應用數學研究所 89751010 91 |
| 資料來源 | http://thesis.lib.nccu.edu.tw/record/#G0089751010 |
| Type | thesis |
| dc.contributor.advisor | 陳天進 | zh_TW |
| dc.contributor.advisor | Ten-ging Chen | en_US |
| dc.contributor.author (Authors) | 謝佩玲 | zh_TW |
| dc.contributor.author (Authors) | Peiling Hsieh | en_US |
| dc.creator (作者) | 謝佩玲 | zh_TW |
| dc.creator (作者) | Peiling Hsieh | en_US |
| dc.date (日期) | 2002 | en_US |
| dc.date.accessioned | 17-Sep-2009 13:44:46 (UTC+8) | - |
| dc.date.available | 17-Sep-2009 13:44:46 (UTC+8) | - |
| dc.date.issued (上傳時間) | 17-Sep-2009 13:44:46 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0089751010 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/32557 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學研究所 | zh_TW |
| dc.description (描述) | 89751010 | zh_TW |
| dc.description (描述) | 91 | zh_TW |
| dc.description.abstract (摘要) | 在這篇論文裡，我們將用Henkin的積分表現法寫出***u=f在C^n上的球域與殼域的解。 除此之外，我們將估計常數C以滿足***-方程的均勻估計，即||u||∞≦C||f||∞。 | zh_TW |
| dc.description.abstract (摘要) | In this thesis, we will write down the Henkin`s solutions of ***u=f for arbitrary ***-closed (0,1)-form f on the open balls and shell domains in C^n, and then proceed to find an explicit upper bound C such that the uniform estimates hold in these domains; that is, ||u||∞≦C||f||∞. | en_US |
| dc.description.tableofcontents | Abstract i 中文摘要 ii 1.Introduction 1 2.General Results 3 3.Integral Representation of Solution on Balls in C^n 8 4.Uniform Estimate for Solution Balls in C^n 10 5.Uniform Estimate for Solution on Shell Domains in C^n 25 References 34 | zh_TW |
| dc.format.extent | 76137 bytes | - |
| dc.format.extent | 98589 bytes | - |
| dc.format.extent | 125631 bytes | - |
| dc.format.extent | 292759 bytes | - |
| dc.format.extent | 94585 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.format.mimetype | application/pdf | - |
| dc.format.mimetype | application/pdf | - |
| dc.format.mimetype | application/pdf | - |
| dc.format.mimetype | application/pdf | - |
| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0089751010 | en_US |
| dc.subject (關鍵詞) | 均勻估計 | zh_TW |
| dc.title (題名) | 殼域上的 -方程解與均勻估計 | zh_TW |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | [1] T. G. Chen, On Henkin`s solution of the ***-problem on | zh_TW |
| dc.relation.reference (參考文獻) | strictly convex domains in C^n, Universtity of California | zh_TW |
| dc.relation.reference (參考文獻) | at Berkeley Ph. D. Thesis, 1985. | zh_TW |
| dc.relation.reference (參考文獻) | [2] T. G. Chen, Geometry of strictly convex domains and an | zh_TW |
| dc.relation.reference (參考文獻) | application to the uniform estimate of the ***-problem, | zh_TW |
| dc.relation.reference (參考文獻) | Trans. Amer. Math. Soc. 347, (1995), 2127-2137. | zh_TW |
| dc.relation.reference (參考文獻) | [3] T. G. Chen and L. J. Lin, Integral representation of | zh_TW |
| dc.relation.reference (參考文獻) | solution for ***u=f and its uniform estimate on ellipsoids, | zh_TW |
| dc.relation.reference (參考文獻) | Soochow Journal of Mathematics 21, (1995), 313-334. | zh_TW |
| dc.relation.reference (參考文獻) | [4] H. Grauert and I. Lieb, Das Ramirezsche Integral und die | zh_TW |
| dc.relation.reference (參考文獻) | Losung der Gleichung im Bereich der beschrankten Formen, | zh_TW |
| dc.relation.reference (參考文獻) | Rice Univ. Studies 56(1970) no. 2, 29-50. | zh_TW |
| dc.relation.reference (參考文獻) | [5] G. M. Henkin, Integral representations of functions | zh_TW |
| dc.relation.reference (參考文獻) | holomorphic in strictly pseudoconvex domains and | zh_TW |
| dc.relation.reference (參考文獻) | applications to the ***-problem, Mat. Sb. 82(124), 300-308 | zh_TW |
| dc.relation.reference (參考文獻) | (1979); Math. U.S.S.R. Sb. 11(1970), 273-281. | zh_TW |
| dc.relation.reference (參考文獻) | [6] G. M. Henkin and J. Leuterer, Theory of functions on complex | zh_TW |
| dc.relation.reference (參考文獻) | manifolds, Birkfauser, Boston, Mass., 1984. | zh_TW |
| dc.relation.reference (參考文獻) | [7] L. Hormander, L^2 estimates and existence theorems for the | zh_TW |
| dc.relation.reference (參考文獻) | *** operator, Acta Math., 113(1965), 82-152. | zh_TW |
| dc.relation.reference (參考文獻) | [8] L. Hormander, Introduction to complex analysis in several | zh_TW |
| dc.relation.reference (參考文獻) | variables, North Holland, Amsterdam, 1973. | zh_TW |
| dc.relation.reference (參考文獻) | [9] N. Kerzman, Holder and L^p estimates for solution of ***u=f | zh_TW |
| dc.relation.reference (參考文獻) | on strongly pseudoconvex domains, Comm. Pure. Appl. Math., | zh_TW |
| dc.relation.reference (參考文獻) | XXIV(1971), 301-380. | zh_TW |
| dc.relation.reference (參考文獻) | [10]S. G. Krantz, Function theory of several complex variables, | zh_TW |
| dc.relation.reference (參考文獻) | 2nd ed. Wadsworth and Brooks, pacific Grove, CA. | zh_TW |
| dc.relation.reference (參考文獻) | [11]S. Long, Comples analysis, Reading, Mass., Addison-Wesley | zh_TW |
| dc.relation.reference (參考文獻) | Pub. Co., 1977. | zh_TW |
| dc.relation.reference (參考文獻) | [12]E. Ramirez, Divisions problem in der komplexen analysis mit | zh_TW |
| dc.relation.reference (參考文獻) | einer Anwendung auf Rand integral darstellung, Math. Ann., | zh_TW |
| dc.relation.reference (參考文獻) | 184(1970), 172-187. | zh_TW |
| dc.relation.reference (參考文獻) | [13]R. M. Range, Holomorphic functions and integral | zh_TW |
| dc.relation.reference (參考文獻) | representations in several complex variables, Springer- | zh_TW |
| dc.relation.reference (參考文獻) | Verlag New York Inc., 1986. | zh_TW |
| dc.relation.reference (參考文獻) | [14]H. Shi, Uniform estimates for the ***-equation on balls, | zh_TW |
| dc.relation.reference (參考文獻) | Proc. of the 1980 Beijing Symp. on differential geometry | zh_TW |
| dc.relation.reference (參考文獻) | and differential equations, Science Press, Beihing, China, | zh_TW |
| dc.relation.reference (參考文獻) | 1982, Gordon and Breach, Science Publisher, Inc., New York, | zh_TW |
| dc.relation.reference (參考文獻) | vol. 3, 1431-1439. | zh_TW |