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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: 2009-09-17 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
    顯示於類別:[應用數學系] 學位論文

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