Iterated function systems and stability of variational problems on self-similar objects
type: Item
instance of: scholarly article
title: Iterated function systems and stability of variational problems on self-similar objects
zbMATH Open document ID: 1220.28003
author: F. Mendivil
author: Uta Freiberg
author: Davide La Torre
published in: Nonlinear Analysis. Real World Applications
publication date: 2011-01-18T00:00:00Z
review text: From the text: ``Many physical phenomena can be described by variational problems. Classical models and techniques to solve these kinds of problems rely on the assumption that a gradient (maybe in some generalized form is defined and that the underlying domain is smooth. However, non-smooth structures appear frequently in physical phenomena creating `irregular' and `rough' objects.'' In this paper, the authors consider a variational optimization problem involving multifunctions, and prove in Theorem 2 a stability result with respect to the Monge-Kantorovich metric. They then apply Theorem 2 to variational problems of the kind above; namely, to variational problems in which the functional is defined on fractals generated by iterated function systems (Corollary~4).
reviewed by: Enrico Zoli
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 49J53
zbMATH DE Number: 5838191
zbMATH Keywords: Hausdorff metric
zbMATH Keywords: Monge-Kantorovich metric
zbMATH Keywords: multifunctions
zbMATH Keywords: variational problems
zbMATH Keywords: iterated function systems
zbMATH Keywords: fractals
zbMATH Keywords: set-valued analysis
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2010.09.006
OpenAlex ID: W2084221618
cites work: Q3731958
cites work: Iterated function systems and the global construction of fractals
cites work: A comparative simulation study on the IFS distribution function estimator
cites work: Approximating distribution functions by iterated function systems
cites work: Iterated function systems on multifunctions and inverse problems
cites work: A generalized fractal transform for measure-valued images
cites work: Measure-Valued Images, Associated Fractal Transforms, and the Affine Self-Similarity of Images
cites work: Union-additive multimeasures and self-similarity
cites work: Fractal vector measures and vector calculus on planar fractal domains.
cites work: Q4431963
cites work: Contractive multifunctions, fixed point inclusions and iterated multifunction systems
cites work: Set-valued analysis
cites work: Arcwise cone-quasiconvex multicriteria optimization
cites work: Scalar characterizations of weakly cone-convex and weakly cone-quasiconvex functions
cites work: Variational Analysis and Generalized Differentiation I
cites work: Variational Analysis
cites work: Analytical properties of measure geometric Krein-Feller-operators on the real line
cites work: Analysis on fractal objects
cites work: On singularity of energy measures on self-similar sets
cites work: Analysis on fractals
cites work: Q4795312
cites work: Gradients on fractals
DOI: 10.1016/J.NONRWA.2010.09.006
description: scientific article; zbMATH DE number 5838191