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Analysis of a nonconvex problem related to signal selective smoothing


Chipot, M; March, R; Rosati, M; Vergara-Caffarelli, G (1997). Analysis of a nonconvex problem related to signal selective smoothing. Mathematical Models and Methods in Applied Sciences, 7(3):313-328.

Abstract

We study some properties of a nonconvex variational problem. We fail to attain the infimum of the functional that has to be minimized. Instead, minimizing sequences develop gradient oscillations which allow them to reduce the value of the functional. We show an existence result for a perturbed nonconvex version of the problem, and we study the qualitative properties of the corresponding minimizer. The pattern of the gradient oscillations for the original nonperturbed problem is analyzed numerically.

Abstract

We study some properties of a nonconvex variational problem. We fail to attain the infimum of the functional that has to be minimized. Instead, minimizing sequences develop gradient oscillations which allow them to reduce the value of the functional. We show an existence result for a perturbed nonconvex version of the problem, and we study the qualitative properties of the corresponding minimizer. The pattern of the gradient oscillations for the original nonperturbed problem is analyzed numerically.

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15 citations in Web of Science®
16 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:signal selective smoothing; nonconvex variational problem; gradient oscillations
Language:English
Date:1997
Deposited On:27 Jul 2010 07:53
Last Modified:06 Dec 2017 20:58
Publisher:World Scientific Publishing
ISSN:0218-2025
Publisher DOI:https://doi.org/10.1142/S0218202597000189
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0880.65050

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