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題名 殼域上的 -方程解與均勻估計
作者 謝佩玲
Peiling Hsieh
貢獻者 陳天進
Ten-ging Chen
謝佩玲
Peiling Hsieh
關鍵詞 均勻估計
日期 2002
上傳時間 17-九月-2009 13:44:46 (UTC+8)
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||∞。
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.
描述 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
資料類型 thesis
dc.contributor.advisor 陳天進zh_TW
dc.contributor.advisor Ten-ging Chenen_US
dc.contributor.author (作者) 謝佩玲zh_TW
dc.contributor.author (作者) Peiling Hsiehen_US
dc.creator (作者) 謝佩玲zh_TW
dc.creator (作者) Peiling Hsiehen_US
dc.date (日期) 2002en_US
dc.date.accessioned 17-九月-2009 13:44:46 (UTC+8)-
dc.date.available 17-九月-2009 13:44:46 (UTC+8)-
dc.date.issued (上傳時間) 17-九月-2009 13:44:46 (UTC+8)-
dc.identifier (其他 識別碼) G0089751010en_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) 89751010zh_TW
dc.description (描述) 91zh_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
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0089751010en_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) thesisen
dc.relation.reference (參考文獻) [1] T. G. Chen, On Henkin`s solution of the ***-problem onzh_TW
dc.relation.reference (參考文獻) strictly convex domains in C^n, Universtity of Californiazh_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 anzh_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 ofzh_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 diezh_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 functionszh_TW
dc.relation.reference (參考文獻) holomorphic in strictly pseudoconvex domains andzh_TW
dc.relation.reference (參考文獻) applications to the ***-problem, Mat. Sb. 82(124), 300-308zh_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 complexzh_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 thezh_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 severalzh_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=fzh_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-Wesleyzh_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 mitzh_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 integralzh_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 geometryzh_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