This article is cited in 15 papers

Conditionally well-posed and generalized well-posed problems

M. Yu. Kokurin

Mari State University, Ioshkar-Ola

Abstract: It is proved that, for a pair of metric spaces, the operators of abstract conditionally well-posed problems admit extensions that are continuous on the original domain with respect to the ambient space. As a corollary, it is shown that an arbitrary conditionally well-posed problem can be regularized via an operator independent of the error level in the input data. Certain applications to ill-posed operator equations and variational problems are discussed.

Key words: ill-posed problem, conditionally well-posed problem, regularizing operator, continuous operator, metric space.

UDC: 519.61

Received: 23.01.2013

DOI: 10.7868/S0044466913060124

 English version: Computational Mathematics and Mathematical Physics, 2013, 53:6, 681–690

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