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

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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

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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