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Various minimization problems involving the total variation in one dimension
Descriptive
TitleInfo
Title
Various minimization problems involving the total variation in one dimension
Name
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Sznigir
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(type = given)
Thomas
NamePart
(type = date)
1987-
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Thomas Sznigir
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author
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Brezis
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Haim
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Haim Brezis
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Advisory Committee
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chair
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Vogelius
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Michael
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Michael Vogelius
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Advisory Committee
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internal member
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(type = family)
Han
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Zheng-Chao
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Zheng-Chao Han
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Advisory Committee
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internal member
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Nguyen
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Hoai-Minh
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Hoai-Minh Nguyen
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Advisory Committee
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outside member
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Rutgers University
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degree grantor
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School of Graduate Studies
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Text
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theses
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2017
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2017-10
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2017
Place
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xx
Language
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eng
Abstract
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We consider certain minimization problems in one dimension. The first one is the ROF filter, which was originally introduced in the context of image processing. For the one-dimensional case, we show that the problem can be reformulated as a variational inequality, and use this to extend existing regularity results. In addition, we look at the jump set of solutions and investigate its behavior as certain parameters are changed. The second functional to be considered arises in the context of regularized interpolation. The second problem is in the context of regularized interpolation, and the functional to be minimized uses the total variation as a penalty term. This problem is shown to be ill-posed with multiple solutions, and the set of solutions is described. Next, we introduce further regularization methods that lead to unique solutions, and use these regularized solutions to determine special solutions of the original problem. Finally, we consider the functional in the space L^2. To investigate it, the lower semicontinuous envelope is constructed. We then characterize the minimizers of the LSC envelope.
Subject
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Topic
Mathematics
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Title
Rutgers University Electronic Theses and Dissertations
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ETD_8365
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electronic resource
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application/pdf
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text/xml
Extent
1 online resource (iv, 132 p. : ill.)
Note
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Ph.D.
Note
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Includes bibliographical references
Subject
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Topic
Variational inequalities (Mathematics)
Note
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by Thomas Sznigir
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School of Graduate Studies Electronic Theses and Dissertations
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rucore10001600001
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NjNbRU
Identifier
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doi:10.7282/T3TX3JHB
Genre
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ETD doctoral
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Rights
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The author owns the copyright to this work.
RightsHolder
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Name
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Sznigir
GivenName
Thomas
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Permission or license
DateTime
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2017-09-19 12:01:59
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Name
Thomas Sznigir
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Affiliation
Rutgers University. School of Graduate Studies
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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2017-09-20T21:35:48
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2017-09-20T21:35:48
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