位场解析延拓的稳定性估计<sup>*</sup>

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位场解析延拓的稳定性估计^*

基金项目: * 国家自然科学基金(19671056);上海市教委基金(96ZA10420)资助课题

1.
P. O. Box 267, East China Geological Institute, Fuzhou, Jiangxi 344000, P. R. China;
2.
Department of Mathematics, Fudan University, Shanghai 200433, P. R. China;
3.
Department of Mathematics, Shanghai University, Shanghai 200072, P. R. China

摘要: 本文讨论两类非典型情形下Laplace方程Cauchy问题解的稳定性,分别利用共形映照、不适定问题的解法(Tikhonov,栾文贵,Yamamoto)相应获得了解的加权H^Lder型稳定性估计和对数型稳定性估计.
- Laplace方程Cauchy问题 /
- 位场解析延拓 /
- 不适定问题 /
- 稳定性估计
Abstract: This paper discusses the stability of solutions to a class of Cauchy pro blems for Laplace equatio ns under two kinds of nonclassical circumstances. By means of conformal mapping and Tikhonov, Luan Wengui and Yamamo to. smethods for solving ill-posed problems respectively, the stability estimations of weighted Hlder type and logarithmic type, have been obtained accor dingly.
- Cauchy problems for Laplace equations /
- analytic continuation of potential field /
- ill-posed problems /
- stability estimation

[1]	L.Nirenberg,Uniqueness in Cauchy problems for differential equations with constant leading coefficients,Comm.Pure Appl.Math.,10(1)(1957),89-115.
[2]	栾文贵著,《地球物理中的反问题》,科学出版社(1989),32-65.
[3]	栾文贵,位场、波场和电磁场的延拓,中国科学(A辑),(9)(1985),824-839.
[4]	李明忠、候宗义、徐振远著,《椭圆型方程组理论和边值问题》,复旦大学出版社(1990),228-231.
[5]	程晋、徐定华,关于一类微分方程反问题的若干讨论,宁夏大学学报(自然科学版),17(1)(1996),74) 75.
[6]	A.N.Tikhonov and V.Y.Arsenin,Solutions of Ill-Posed Problems,V.H.Winston and Sons(1977),27) 32.
[7]	M.Yamamo to,Conditional stability in determination of force terms of heat equations in arectangle,Math.Comput.Modelling,18(1)(1993),79-88.
[8]	河田龙夫著,《Fourier分析》,周民强译,高等教育出版社(1982),108-112.

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