Geodesic
Conditionally well-posed and generalized well-posed problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 6, pp. 857-866

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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. 
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     author = {M. Yu. Kokurin},
     title = {Conditionally well-posed and generalized well-posed problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {53},
     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a2/}
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M. Yu. Kokurin. Conditionally well-posed and generalized well-posed problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 6, pp. 857-866. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a2/