On a level-set method for Ill-posed problems with piecewise nonconstant coefficients
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 Tikho...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2012 |
| País: | Brasil |
| Institución: | Universidade Federal do Rio Grande (FURG) |
| Repositorio: | Repositório Institucional da FURG (RI FURG) |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.furg.br:1/3538 |
| Acceso en línea: | http://repositorio.furg.br/handle/1/3538 |
| Access Level: | acceso abierto |
| Palabra clave: | Level set methods Regularization Ill-posed problems Piecewise Non-constant coefficients |
| Sumario: | 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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