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Spectral Regularization Methods for an Abstract Ill-Posed Elliptic Problem

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  • Nadjib Boussetila
  • Salim Hamida
  • Faouzia Rebbani

Abstract

We study an abstract elliptic Cauchy problem associated with an unbounded self-adjoint positive operator which has a continuous spectrum. It is well-known that such a problem is severely ill-posed; that is, the solution does not depend continuously on the Cauchy data. We propose two spectral regularization methods to construct an approximate stable solution to our original problem. Finally, some other convergence results including some explicit convergence rates are also established under a priori bound assumptions on the exact solution.

Suggested Citation

  • Nadjib Boussetila & Salim Hamida & Faouzia Rebbani, 2013. "Spectral Regularization Methods for an Abstract Ill-Posed Elliptic Problem," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, November.
    • Handle: RePEc:hin:jnlaaa:947379
    DOI: 10.1155/2013/947379
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