政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32557

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32557

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政大典藏 > College of Science > Department of Mathematical Sciences > Theses > Item 140.119/32557

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/32557

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)
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
Appears in Collections:	[Department of Mathematical Sciences] Theses

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