On a Level-Set Method for Ill-Posed Problems with Piecewise Nonconstant Coefficients
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-01-31
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
De Cezaro, A.. 2013. On a Level-Set Method for Ill-Posed Problems with Piecewise Nonconstant Coefficients. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-15.
https://search.emarefa.net/detail/BIM-447432
Modern Language Association (MLA)
De Cezaro, A.. On a Level-Set Method for Ill-Posed Problems with Piecewise Nonconstant Coefficients. Journal of Applied Mathematics No. 2013 (2013), pp.1-15.
https://search.emarefa.net/detail/BIM-447432
American Medical Association (AMA)
De Cezaro, A.. On a Level-Set Method for Ill-Posed Problems with Piecewise Nonconstant Coefficients. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-15.
https://search.emarefa.net/detail/BIM-447432
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-447432