New trends in shape optimization. (2015)

• Record Type: Book
• Further Information: Note: Also Pratelli, Günter Leugering.
• Editors: Pratelli, Aldo; Leugering, Günter, 1953-
• 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.
• Publisher Details: Cham : Birkhäuser
• Publication Date: 2015
• Extent: 1 online resource
• Subjects: 514/.24; Mathematics; Shape theory (Topology); Mathematical optimization; MATHEMATICS -- Topology; Mathematical optimization; Shape theory (Topology); Science -- System Theory; Cybernetics & systems theory; Differential equations, partial; Systems theory; Mathematics -- Differential Equations; Differential calculus & equations; Electronic books
• Languages: English
• ISBNs: 9783319175638; 3319175637
• Related ISBNs: 9783319175621; 3319175629
• Notes: 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.; Note: 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.; Note: Online resource; title from PDF title page (EBSCO, viewed December 30, 2015).
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