Open Access
2013 Spectral Regularization Methods for an Abstract Ill-Posed Elliptic Problem
Nadjib Boussetila, Salim Hamida, Faouzia Rebbani
Abstr. Appl. Anal. 2013: 1-11 (2013). DOI: 10.1155/2013/947379


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.


Download Citation

Nadjib Boussetila. Salim Hamida. Faouzia Rebbani. "Spectral Regularization Methods for an Abstract Ill-Posed Elliptic Problem." Abstr. Appl. Anal. 2013 1 - 11, 2013.


Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 07095524
MathSciNet: MR3132526
Digital Object Identifier: 10.1155/2013/947379

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
Back to Top