Ill-Posedness of sublinear minimization problems
It is well known that minimization problems involving sublinear regularization terms are ill-posed, in Sobolev spaces. Extended results to spaces of bounded variation functions BV were recently showed in the special case of bounded regularization terms. In this note, a generalization to sublinear re...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2011-04-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X11000071 |
| Summary: | It is well known that minimization problems involving sublinear regularization terms are ill-posed, in Sobolev spaces. Extended results to spaces of bounded variation functions BV were recently showed in the special case of bounded regularization terms. In this note, a generalization to sublinear regularization is presented in BV spaces. Notice that our results are optimal in the sense that linear regularization leads to well-posed minimization problems in BV spaces. |
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| ISSN: | 1110-256X |