Simplified excision techniques for free discontinuity problems in several variables
type: Item
instance of: scholarly article
title: Simplified excision techniques for free discontinuity problems in several variables
zbMATH Open document ID: 0891.49007
author: Sergio Solimini
published in: Journal of Functional Analysis
publication date: 1998-07-09T00:00:00Z
review text: The author studied the free discontinuity problems. These are problems where an unknown discontinuity set can be found by solving a minimization problem. These kind of problems appear in the theory of image segmentation. The author has found applications to problems in several variables thanks to a Sobolev type theorem which ensures the Hölder continuity of certain functions out of a suitable neighbourhood of their discontinuity set.
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 49J10
zbMATH DE Number: 1106587
zbMATH Keywords: minimization
zbMATH Keywords: second order elliptic equations
zbMATH Keywords: free discontinuity problems
zbMATH Keywords: image segmentation
reviewed by: Sebastian Aniţa
MaRDI profile type: Publication
full work available at URL: jfan.1996.3081
OpenAlex ID: W2023513405
cites work: Q4710887
cites work: Existence theory for a new class of variational problems
cites work: Q4731718
cites work: A variational method in image segmentation: Existence and approximation results
cites work: On the singular sets of minimizers of the Mumford-Shah functional
cites work: Uniform rectifiability and singular sets
cites work: Q3202752
cites work: Existence theorem for a minimum problem with free discontinuity set
cites work: Unform rectifiability of image segmentations obtained by a variational method
cites work: Q3986708
cites work: Q5565773
cites work: Q3905599
cites work: Variational methods in image segmentation with 7 image processing experiments
cites work: Q5518064
cites work: Optimal approximations by piecewise smooth functions and associated variational problems
DOI: 10.1006/JFAN.1996.3081
description: scientific article; zbMATH DE number 1106587