## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2013, Special Issue (2012), Article ID 123643, 15 pages.

### On a Level-Set Method for Ill-Posed Problems with Piecewise Nonconstant Coefficients

A. De Cezaro

#### Abstract

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.

#### Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2012), Article ID 123643, 15 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394806090

Digital Object Identifier
doi:10.1155/2013/123643

Mathematical Reviews number (MathSciNet)
MR3029965

Zentralblatt MATH identifier
1266.47027

#### Citation

De Cezaro, A. On a Level-Set Method for Ill-Posed Problems with Piecewise Nonconstant Coefficients. J. Appl. Math. 2013, Special Issue (2012), Article ID 123643, 15 pages. doi:10.1155/2013/123643. https://projecteuclid.org/euclid.jam/1394806090

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