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The Regularity Theory for the Mumford-Shah Functional on the Plane

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Title: The Regularity Theory for the Mumford-Shah Functional on the Plane
Description: This book provides a thorough and up-to-date account of the state of art of the regularity theory for minimizers of the Mumford–Shah functional of image segmentation in the 2-dimensional setting. Starting with some classical preliminary results, which settle the issue of existence of minimizing couples (u,K), the structure of the set K is then analyzed by using ε-regularity theorems. Several consequences of the latter are also investigated, in particular leading to different characterizations of the Mumford–Shah conjecture. The proofs are given with full details, often revisiting the relevant literature and introducing new arguments.
Authors: Camillo De Lellis, Matteo Focardi
Resource Type: eBook.
Subjects: Mathematical optimization, Calculus of variations
Categories: MATHEMATICS / Functional Analysis, MATHEMATICS / Differential Equations / General, MATHEMATICS / Mathematical Analysis
Database: eBook Collection (EBSCOhost)
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  – Type: ebook-pdf
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Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 4154976
RelevancyScore: 1129
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1129.38305664063
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  Data: The Regularity Theory for the Mumford-Shah Functional on the Plane
– Name: Abstract
  Label: Description
  Group: Ab
  Data: This book provides a thorough and up-to-date account of the state of art of the regularity theory for minimizers of the Mumford–Shah functional of image segmentation in the 2-dimensional setting. Starting with some classical preliminary results, which settle the issue of existence of minimizing couples (u,K), the structure of the set K is then analyzed by using ε-regularity theorems. Several consequences of the latter are also investigated, in particular leading to different characterizations of the Mumford–Shah conjecture. The proofs are given with full details, often revisiting the relevant literature and introducing new arguments.
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  Data: <searchLink fieldCode="AR" term="%22Camillo+De+Lellis%2C+Matteo+Focardi%22">Camillo De Lellis, Matteo Focardi</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Calculus+of+variations%22">Calculus of variations</searchLink>
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  Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Functional+Analysis%22">MATHEMATICS / Functional Analysis</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Differential+Equations+%2F+General%22">MATHEMATICS / Differential Equations / General</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Mathematical+Analysis%22">MATHEMATICS / Mathematical Analysis</searchLink>
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  BibEntity:
    Classifications:
      – Code: 510
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Mathematical optimization
        Type: general
      – SubjectFull: Calculus of variations
        Type: general
    Titles:
      – TitleFull: The Regularity Theory for the Mumford-Shah Functional on the Plane
        Type: main
  BibRelationships:
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      – PersonEntity:
          Name:
            NameFull: Camillo De Lellis, Matteo Focardi
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          Name:
            NameFull: Camillo De Lellis, Matteo Focardi
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2025
            – D: 24
              M: 07
              Type: profile
              Y: 2025
          Identifiers:
            – Type: isbn-print
              Value: 9783985470891
            – Type: isbn-electronic
              Value: 9783985475896
          Titles:
            – TitleFull: The Regularity Theory for the Mumford-Shah Functional on the Plane
              Type: main
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