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    Title: 殼域上的 -方程解與均勻估計
    Authors: 謝佩玲
    Peiling Hsieh
    Contributors: 陳天進
    Ten-ging Chen
    謝佩玲
    Peiling Hsieh
    Keywords: 均勻估計
    Date: 2002
    Issue Date: 2009-09-17 13:44:46 (UTC+8)
    Description.abstract: 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||∞.
    Reference: [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
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0089751010
    Data Type: thesis
    DCField Value Language
    dc.contributor.advisor 陳天進zh_TW
    dc.contributor.advisor Ten-ging Chenen_US
    dc.contributor.author 謝佩玲zh_TW
    dc.contributor.author Peiling Hsiehen_US
    dc.creator (Authors) 謝佩玲zh_TW
    dc.creator (Authors) Peiling Hsiehen_US
    dc.date (Date) 2002en_US
    dc.date.accessioned 2009-09-17 13:44:46 (UTC+8)-
    dc.date.available 2009-09-17 13:44:46 (UTC+8)-
    dc.date.issued (Issue Date) 2009-09-17 13:44:46 (UTC+8)-
    dc.identifier (Other Identifiers) G0089751010en_US
    dc.identifier.uri (URI) http://nccuir.lib.nccu.edu.tw/handle/140.119/32557-
    dc.description (Description) 碩士zh_TW
    dc.description (Description) 國立政治大學zh_TW
    dc.description (Description) 應用數學研究所zh_TW
    dc.description (Description) 89751010zh_TW
    dc.description (Description) 91zh_TW
    dc.description.abstract (Abstract) 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 (Abstract) 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.format.extent 292759 bytes-
    dc.format.extent 94585 bytes-
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    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 (Source URI) http://thesis.lib.nccu.edu.tw/record/#G0089751010en_US
    dc.subject (Keywords) 均勻估計zh_TW
    dc.title (Title) 殼域上的 -方程解與均勻估計zh_TW
    dc.type (Data Type) thesisen
    dc.relation.reference (Reference) [1] T. G. Chen, On Henkin's solution of the ***-problem onzh_TW
    dc.relation.reference (Reference) strictly convex domains in C^n, Universtity of Californiazh_TW
    dc.relation.reference (Reference) at Berkeley Ph. D. Thesis, 1985.zh_TW
    dc.relation.reference (Reference) [2] T. G. Chen, Geometry of strictly convex domains and anzh_TW
    dc.relation.reference (Reference) application to the uniform estimate of the ***-problem,zh_TW
    dc.relation.reference (Reference) Trans. Amer. Math. Soc. 347, (1995), 2127-2137.zh_TW
    dc.relation.reference (Reference) [3] T. G. Chen and L. J. Lin, Integral representation ofzh_TW
    dc.relation.reference (Reference) solution for ***u=f and its uniform estimate on ellipsoids,zh_TW
    dc.relation.reference (Reference) Soochow Journal of Mathematics 21, (1995), 313-334.zh_TW
    dc.relation.reference (Reference) [4] H. Grauert and I. Lieb, Das Ramirezsche Integral und diezh_TW
    dc.relation.reference (Reference) Losung der Gleichung im Bereich der beschrankten Formen,zh_TW
    dc.relation.reference (Reference) Rice Univ. Studies 56(1970) no. 2, 29-50.zh_TW
    dc.relation.reference (Reference) [5] G. M. Henkin, Integral representations of functionszh_TW
    dc.relation.reference (Reference) holomorphic in strictly pseudoconvex domains andzh_TW
    dc.relation.reference (Reference) applications to the ***-problem, Mat. Sb. 82(124), 300-308zh_TW
    dc.relation.reference (Reference) (1979); Math. U.S.S.R. Sb. 11(1970), 273-281.zh_TW
    dc.relation.reference (Reference) [6] G. M. Henkin and J. Leuterer, Theory of functions on complexzh_TW
    dc.relation.reference (Reference) manifolds, Birkfauser, Boston, Mass., 1984.zh_TW
    dc.relation.reference (Reference) [7] L. Hormander, L^2 estimates and existence theorems for thezh_TW
    dc.relation.reference (Reference) *** operator, Acta Math., 113(1965), 82-152.zh_TW
    dc.relation.reference (Reference) [8] L. Hormander, Introduction to complex analysis in severalzh_TW
    dc.relation.reference (Reference) variables, North Holland, Amsterdam, 1973.zh_TW
    dc.relation.reference (Reference) [9] N. Kerzman, Holder and L^p estimates for solution of ***u=fzh_TW
    dc.relation.reference (Reference) on strongly pseudoconvex domains, Comm. Pure. Appl. Math.,zh_TW
    dc.relation.reference (Reference) XXIV(1971), 301-380.zh_TW
    dc.relation.reference (Reference) [10]S. G. Krantz, Function theory of several complex variables,zh_TW
    dc.relation.reference (Reference) 2nd ed. Wadsworth and Brooks, pacific Grove, CA.zh_TW
    dc.relation.reference (Reference) [11]S. Long, Comples analysis, Reading, Mass., Addison-Wesleyzh_TW
    dc.relation.reference (Reference) Pub. Co., 1977.zh_TW
    dc.relation.reference (Reference) [12]E. Ramirez, Divisions problem in der komplexen analysis mitzh_TW
    dc.relation.reference (Reference) einer Anwendung auf Rand integral darstellung, Math. Ann.,zh_TW
    dc.relation.reference (Reference) 184(1970), 172-187.zh_TW
    dc.relation.reference (Reference) [13]R. M. Range, Holomorphic functions and integralzh_TW
    dc.relation.reference (Reference) representations in several complex variables, Springer-zh_TW
    dc.relation.reference (Reference) Verlag New York Inc., 1986.zh_TW
    dc.relation.reference (Reference) [14]H. Shi, Uniform estimates for the ***-equation on balls,zh_TW
    dc.relation.reference (Reference) Proc. of the 1980 Beijing Symp. on differential geometryzh_TW
    dc.relation.reference (Reference) and differential equations, Science Press, Beihing, China,zh_TW
    dc.relation.reference (Reference) 1982, Gordon and Breach, Science Publisher, Inc., New York,zh_TW
    dc.relation.reference (Reference) vol. 3, 1431-1439.zh_TW

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