Applied Mathematics and Mechanics (English Edition) ›› 1998, Vol. 19 ›› Issue (6): 563-572.

• 论文 • 上一篇    下一篇

ON THE STABILITY ESTIMATION OF ANALYTIC CONTINUATION FOR POTENTIAL FIELD

徐定华1, 程晋2, 李明忠3   

  1. 1. P. O. Box 267, East China Geological institute, Fuzhou 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
  • 收稿日期:1996-09-20 出版日期:1998-06-18 发布日期:1998-06-18
  • 基金资助:
    Project supported by the National Science Foundation of China and the Science Foundation of Shanghai Education Committee, P. R. China

ON THE STABILITY ESTIMATION OF ANALYTIC CONTINUATION FOR POTENTIAL FIELD

Xu Dinghua1, Cheng Jin2, Li Mingzhong3   

  1. 1. P. O. Box 267, East China Geological institute, Fuzhou 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
  • Received:1996-09-20 Online:1998-06-18 Published:1998-06-18
  • Supported by:
    Project supported by the National Science Foundation of China and the Science Foundation of Shanghai Education Committee, P. R. China

摘要: This paper discusses the stability of solutions to a class of Cauchy problems forLap lace equations under two kinds of nonclassical circumstances. By means ofconformal mapping and Tikhonov. Luan bangui and Yamamoto’s methods.for solvingill-posed problems respectively, the stability estimations of weighted Holder type andlogarithmic type, have been obtained accordingly.

关键词: Cauchy problems for Laplace equations, analytic continuation ofpotential field, ill-posed problems, stability estimation

Abstract: This paper discusses the stability of solutions to a class of Cauchy problems forLap lace equations under two kinds of nonclassical circumstances. By means ofconformal mapping and Tikhonov. Luan bangui and Yamamoto’s methods.for solvingill-posed problems respectively, the stability estimations of weighted Holder type andlogarithmic type, have been obtained accordingly.

Key words: Cauchy problems for Laplace equations, analytic continuation ofpotential field, ill-posed problems, stability estimation

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