New trends in shape optimization [electronic resource] / Also Pratelli, Günter Leugering.
Pratelli, Aldo, editor.; Leugering, Günter, 1953- editor.
2015
QA612.7
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Title
New trends in shape optimization [electronic resource] / Also Pratelli, Günter Leugering.
ISBN
9783319175638 electronic book
3319175637 electronic book
9783319175621
3319175629
Published
Cham : Birkhäuser, 2015.
Language
English
Description
1 online resource.
Call Number
QA612.7
Dewey Decimal Classification
514/.24
Bibliography, etc. 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
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (viewed December 30, 2015)
Added Author
Pratelli, Aldo, editor.
Leugering, Günter, 1953- editor.
Series
International series of numerical mathematics ; 166.
Available in Other Form
Print version: 9783319175621
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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
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

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