On a level-set method for Ill-posed problems with piecewise nonconstant coefficients

Detalhes bibliográficos
Autor(a) principal: Cezaro, Adriano de
Data de Publicação: 2012
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da FURG (RI FURG)
Texto Completo: http://repositorio.furg.br/handle/1/3538
Resumo: We investigate a level-set type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable approximate solutions of the inverse problem we propose a Tikhonov-type regularization approach coupled with a level set framework. We prove the existence of generalized minimizers for the Tikhonov functional. Moreover, we prove convergence and stability for regularized solutions with respect to the noise level, characterizing the level-set approach as a regularization method for inverse problems. We also show the applicability of the proposed level set method in some interesting inverse problems arising in elliptic PDE models.
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spelling On a level-set method for Ill-posed problems with piecewise nonconstant coefficientsLevel set methodsRegularizationIll-posed problemsPiecewise Non-constant coefficientsWe investigate a level-set type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable approximate solutions of the inverse problem we propose a Tikhonov-type regularization approach coupled with a level set framework. We prove the existence of generalized minimizers for the Tikhonov functional. Moreover, we prove convergence and stability for regularized solutions with respect to the noise level, characterizing the level-set approach as a regularization method for inverse problems. We also show the applicability of the proposed level set method in some interesting inverse problems arising in elliptic PDE models.2013-06-17T18:27:40Z2013-06-17T18:27:40Z2012info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfCEZARO, Adriano de. On a level-set method for Ill-posed problems with piecewise nonconstant coefficients. Journal of Applied Mathematics, v. 2, p. 1- 23, 2012. Disponível em: <http://arxiv.org/pdf/1207.2572v2.pdf>. Acesso em: 28 fev. 2013.http://repositorio.furg.br/handle/1/3538engCezaro, Adriano deinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da FURG (RI FURG)instname:Universidade Federal do Rio Grande (FURG)instacron:FURG2013-06-17T18:27:40Zoai:repositorio.furg.br:1/3538Repositório InstitucionalPUBhttps://repositorio.furg.br/oai/request || http://200.19.254.174/oai/requestopendoar:2013-06-17T18:27:40Repositório Institucional da FURG (RI FURG) - Universidade Federal do Rio Grande (FURG)false
dc.title.none.fl_str_mv On a level-set method for Ill-posed problems with piecewise nonconstant coefficients
title On a level-set method for Ill-posed problems with piecewise nonconstant coefficients
spellingShingle On a level-set method for Ill-posed problems with piecewise nonconstant coefficients
Cezaro, Adriano de
Level set methods
Regularization
Ill-posed problems
Piecewise Non-constant coefficients
title_short On a level-set method for Ill-posed problems with piecewise nonconstant coefficients
title_full On a level-set method for Ill-posed problems with piecewise nonconstant coefficients
title_fullStr On a level-set method for Ill-posed problems with piecewise nonconstant coefficients
title_full_unstemmed On a level-set method for Ill-posed problems with piecewise nonconstant coefficients
title_sort On a level-set method for Ill-posed problems with piecewise nonconstant coefficients
author Cezaro, Adriano de
author_facet Cezaro, Adriano de
author_role author
dc.contributor.author.fl_str_mv Cezaro, Adriano de
dc.subject.por.fl_str_mv Level set methods
Regularization
Ill-posed problems
Piecewise Non-constant coefficients
topic Level set methods
Regularization
Ill-posed problems
Piecewise Non-constant coefficients
description We investigate a level-set type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable approximate solutions of the inverse problem we propose a Tikhonov-type regularization approach coupled with a level set framework. We prove the existence of generalized minimizers for the Tikhonov functional. Moreover, we prove convergence and stability for regularized solutions with respect to the noise level, characterizing the level-set approach as a regularization method for inverse problems. We also show the applicability of the proposed level set method in some interesting inverse problems arising in elliptic PDE models.
publishDate 2012
dc.date.none.fl_str_mv 2012
2013-06-17T18:27:40Z
2013-06-17T18:27:40Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv CEZARO, Adriano de. On a level-set method for Ill-posed problems with piecewise nonconstant coefficients. Journal of Applied Mathematics, v. 2, p. 1- 23, 2012. Disponível em: <http://arxiv.org/pdf/1207.2572v2.pdf>. Acesso em: 28 fev. 2013.
http://repositorio.furg.br/handle/1/3538
identifier_str_mv CEZARO, Adriano de. On a level-set method for Ill-posed problems with piecewise nonconstant coefficients. Journal of Applied Mathematics, v. 2, p. 1- 23, 2012. Disponível em: <http://arxiv.org/pdf/1207.2572v2.pdf>. Acesso em: 28 fev. 2013.
url http://repositorio.furg.br/handle/1/3538
dc.language.iso.fl_str_mv eng
language eng
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dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Institucional da FURG (RI FURG)
instname:Universidade Federal do Rio Grande (FURG)
instacron:FURG
instname_str Universidade Federal do Rio Grande (FURG)
instacron_str FURG
institution FURG
reponame_str Repositório Institucional da FURG (RI FURG)
collection Repositório Institucional da FURG (RI FURG)
repository.name.fl_str_mv Repositório Institucional da FURG (RI FURG) - Universidade Federal do Rio Grande (FURG)
repository.mail.fl_str_mv
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