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The Resource New trends in shape optimization, Also Pratelli, Günter Leugering, (electronic book)

New trends in shape optimization, Also Pratelli, Günter Leugering, (electronic book)

Work
Publication
Extent
1 online resource.
Contents
  • Introduction; On the Minimization of Area Among Chord-Convex Sets; 1 Introduction and Setting of the Problem; 2 Definitions and Results; 2.1 Uniqueness of the Bisecting Chord of Given Direction; 2.2 Properties of the Extreme Points and of the Intersections Between Chords; 2.3 Zindler Sets and Their Properties; References; Optimization Problems Involving the First Dirichlet Eigenvalue and the Torsional Rigidity; 1 Introduction; 2 Statement of the Problem; 3 A Sharp Inequality Between Torsion and First Eigenvalue; 4 The Attainable Set; 5 Torsional Rigidity and the Heat Equation
  • 4.2 Parametrize Functions by Geometries5 Metric Structures via Characteristic Functions of Measurable Sets; 5.1 Linfty-Convergence of Measurable Sets; 5.2 Lp-Convergence of Measurable Sets, 1lep<infty; 5.3 Compact Families; 6 Metric Structures via Distance Functions; 6.1 Pompéiu's Ecart Mutuel and Hausdorff Metric on Compact Sets; 6.2 Metric of Uniform Convergence; 6.3 Metric of Lipschitz Convergence; 6.4 Metric of W1,p-Convergence, 1lep<infty; 6.5 Metrics Compatible with the Abelian Group Structure; 7 Metric Structures via Oriented Distance Functions
  • 7.1 Oriented Distance Function: Definition and Some Properties7.2 Some General Metrics on Cb(D); 7.3 Metrics Compatible with the Abelian Group Structure; 8 Boundary Properties of Sets in Cb0(D); 8.1 Finite Perimeter or Caccioppoli Sets; 8.2 Preliminary Considerations; 8.3 Sets of Bounded Curvature; 8.4 Metrics for Families of Sets with Smooth Boundaries; 9 Sets of Positive Reach, Submanifolds, Squared Distance Functions; 9.1 Sets of Positive Reach; 9.2 Ck-Submanifolds, kge2; 9.3 Metric on Families of Submanifolds; 10 Metric Structure via the Support Function; 11 Some Concluding Remarks
Isbn
9783319175621
Instance
Label
New trends in shape optimization
Title
New trends in shape optimization
Statement of responsibility
Also Pratelli, Günter Leugering
Contributor
Editor
Subject
Language
eng
Member of
Cataloging source
N$T
Dewey number
514/.24
Index
no index present
LC call number
QA612.7
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorDate
1953-
http://library.link/vocab/relatedWorkOrContributorName
  • Pratelli, Aldo
  • Leugering, Günter
Series statement
International series of numerical mathematics
Series volume
166
http://library.link/vocab/subjectName
  • Shape theory (Topology)
  • Mathematical optimization
Label
New trends in shape optimization, Also Pratelli, Günter Leugering, (electronic book)
Instantiates
Publication
Antecedent source
unknown
Bibliography note
  • ReferencesOn a Classical Spectral Optimization Problem in Linear Elasticity; 1 Introduction; 2 The Eigenvalue Problems; 3 Analyticity Results ; 4 Isovolumetric Perturbations; References; Metric Spaces of Shapes and Geometries Constructed from Set Parametrized Functions; 1 Introduction; 2 Group, Symmetric Difference, and Characteristic Functions; 2.1 Group Structure Induced by the Symmetric Difference; 2.2 Metric Structures via Characteristic Functions; 3 Parametrize Geometries by Functions: Hypographs; 4 Analytical Representations of Geometries; 4.1 Parametrize Geometries by Functions
  • ReferencesA Phase Field Approach for Shape and Topology Optimization in Stokes Flow; 1 Introduction; 2 Porous Medium---Phase Field Formulation; 3 Sharp Interface Problem; 4 Sharp Interface Limit; References; An Overview on the Cheeger Problem; 1 Introduction; 2 Some Motivations; 2.1 Estimating the Smallest Eigenvalue of the Laplacian; 2.2 Existence of Graphs with Prescribed Mean Curvature; 2.3 Stable Shapes for Total Variation Minimization; 3 Some General Results on the Cheeger Problem; 3.1 The Cheeger Problem in Convex Domains; 3.2 Some Further Results About Cheeger Sets in mathbbR2
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Introduction; On the Minimization of Area Among Chord-Convex Sets; 1 Introduction and Setting of the Problem; 2 Definitions and Results; 2.1 Uniqueness of the Bisecting Chord of Given Direction; 2.2 Properties of the Extreme Points and of the Intersections Between Chords; 2.3 Zindler Sets and Their Properties; References; Optimization Problems Involving the First Dirichlet Eigenvalue and the Torsional Rigidity; 1 Introduction; 2 Statement of the Problem; 3 A Sharp Inequality Between Torsion and First Eigenvalue; 4 The Attainable Set; 5 Torsional Rigidity and the Heat Equation
  • 4.2 Parametrize Functions by Geometries5 Metric Structures via Characteristic Functions of Measurable Sets; 5.1 Linfty-Convergence of Measurable Sets; 5.2 Lp-Convergence of Measurable Sets, 1lep<infty; 5.3 Compact Families; 6 Metric Structures via Distance Functions; 6.1 Pompéiu's Ecart Mutuel and Hausdorff Metric on Compact Sets; 6.2 Metric of Uniform Convergence; 6.3 Metric of Lipschitz Convergence; 6.4 Metric of W1,p-Convergence, 1lep<infty; 6.5 Metrics Compatible with the Abelian Group Structure; 7 Metric Structures via Oriented Distance Functions
  • 7.1 Oriented Distance Function: Definition and Some Properties7.2 Some General Metrics on Cb(D); 7.3 Metrics Compatible with the Abelian Group Structure; 8 Boundary Properties of Sets in Cb0(D); 8.1 Finite Perimeter or Caccioppoli Sets; 8.2 Preliminary Considerations; 8.3 Sets of Bounded Curvature; 8.4 Metrics for Families of Sets with Smooth Boundaries; 9 Sets of Positive Reach, Submanifolds, Squared Distance Functions; 9.1 Sets of Positive Reach; 9.2 Ck-Submanifolds, kge2; 9.3 Metric on Families of Submanifolds; 10 Metric Structure via the Support Function; 11 Some Concluding Remarks
Control code
SPR931873412
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319175621
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Reproduction note
Electronic resource.
Sound
unknown sound
Specific material designation
remote
Label
New trends in shape optimization, Also Pratelli, Günter Leugering, (electronic book)
Publication
Antecedent source
unknown
Bibliography note
  • ReferencesOn a Classical Spectral Optimization Problem in Linear Elasticity; 1 Introduction; 2 The Eigenvalue Problems; 3 Analyticity Results ; 4 Isovolumetric Perturbations; References; Metric Spaces of Shapes and Geometries Constructed from Set Parametrized Functions; 1 Introduction; 2 Group, Symmetric Difference, and Characteristic Functions; 2.1 Group Structure Induced by the Symmetric Difference; 2.2 Metric Structures via Characteristic Functions; 3 Parametrize Geometries by Functions: Hypographs; 4 Analytical Representations of Geometries; 4.1 Parametrize Geometries by Functions
  • ReferencesA Phase Field Approach for Shape and Topology Optimization in Stokes Flow; 1 Introduction; 2 Porous Medium---Phase Field Formulation; 3 Sharp Interface Problem; 4 Sharp Interface Limit; References; An Overview on the Cheeger Problem; 1 Introduction; 2 Some Motivations; 2.1 Estimating the Smallest Eigenvalue of the Laplacian; 2.2 Existence of Graphs with Prescribed Mean Curvature; 2.3 Stable Shapes for Total Variation Minimization; 3 Some General Results on the Cheeger Problem; 3.1 The Cheeger Problem in Convex Domains; 3.2 Some Further Results About Cheeger Sets in mathbbR2
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Introduction; On the Minimization of Area Among Chord-Convex Sets; 1 Introduction and Setting of the Problem; 2 Definitions and Results; 2.1 Uniqueness of the Bisecting Chord of Given Direction; 2.2 Properties of the Extreme Points and of the Intersections Between Chords; 2.3 Zindler Sets and Their Properties; References; Optimization Problems Involving the First Dirichlet Eigenvalue and the Torsional Rigidity; 1 Introduction; 2 Statement of the Problem; 3 A Sharp Inequality Between Torsion and First Eigenvalue; 4 The Attainable Set; 5 Torsional Rigidity and the Heat Equation
  • 4.2 Parametrize Functions by Geometries5 Metric Structures via Characteristic Functions of Measurable Sets; 5.1 Linfty-Convergence of Measurable Sets; 5.2 Lp-Convergence of Measurable Sets, 1lep<infty; 5.3 Compact Families; 6 Metric Structures via Distance Functions; 6.1 Pompéiu's Ecart Mutuel and Hausdorff Metric on Compact Sets; 6.2 Metric of Uniform Convergence; 6.3 Metric of Lipschitz Convergence; 6.4 Metric of W1,p-Convergence, 1lep<infty; 6.5 Metrics Compatible with the Abelian Group Structure; 7 Metric Structures via Oriented Distance Functions
  • 7.1 Oriented Distance Function: Definition and Some Properties7.2 Some General Metrics on Cb(D); 7.3 Metrics Compatible with the Abelian Group Structure; 8 Boundary Properties of Sets in Cb0(D); 8.1 Finite Perimeter or Caccioppoli Sets; 8.2 Preliminary Considerations; 8.3 Sets of Bounded Curvature; 8.4 Metrics for Families of Sets with Smooth Boundaries; 9 Sets of Positive Reach, Submanifolds, Squared Distance Functions; 9.1 Sets of Positive Reach; 9.2 Ck-Submanifolds, kge2; 9.3 Metric on Families of Submanifolds; 10 Metric Structure via the Support Function; 11 Some Concluding Remarks
Control code
SPR931873412
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319175621
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Reproduction note
Electronic resource.
Sound
unknown sound
Specific material designation
remote

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