WIAS Preprint No. 430, (1998)

Local Estimation for an Integral Equation of First Kind with Analytic Kernel



Authors

  • Cheng, Jin
  • Prößdorf, Siegfried
  • Yamamoto, Masashiro

2010 Mathematics Subject Classification

  • 45A05 45H05 45M10

Keywords

  • First kind integral equation, Riesz kernel, analytic kernel, pointwise estimate for the solution severly ill-posed, Cauchy problem, Laplace equation

Abstract

In this paper, an integral equation of the first kind with Riesz kernel is discussed. Since the kernel of this integral equation is analytic, this problem is severe ill-posed. We prove that, for solutions of the integral equation, a local conditional pointwise estimate holds at a point if the solution has some additional smoothness properties in a neighbourhood of this point.

Appeared in

  • J. Inverse and Ill-Posed Problems, 6 (1998), pp. 115-126

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