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New Trends in Shape Optimization

  • Book
  • © 2015

Overview

Editors:
  1. Aldo Pratelli

    1. Department Mathematik, Universität Erlangen‐Nürnberg, Erlangen, Germany

  2. Günter Leugering

    1. Department Mathematik, Universität Erlangen-Nürnberg, Erlangen, Germany

  • Plenty of modern problems, also including many open ones
  • State-of-the-art description of research a shape optimization
  • Clearly written, easily accessible contributions
  • Includes supplementary material: sn.pub/extras

Part of the book series: International Series of Numerical Mathematics (ISNM, volume 166)

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About this book

This volume reflects “New Trends in Shape Optimization” and is based on a workshop of the same name organized at the Friedrich-Alexander University Erlangen-Nürnberg in September 2013. During the workshop senior mathematicians and young scientists alike presented their latest findings. The format of the meeting allowed fruitful discussions on challenging open problems, and triggered a number of new and spontaneous collaborations. As such, the idea was born to produce this book, each chapter of which was written by a workshop participant, often with a collaborator. The content of the individual chapters ranges from survey papers to original articles; some focus on the topics discussed at the Workshop, while others involve arguments outside its scope but which are no less relevant for the field today. As such, the book offers readers a balanced introduction to the emerging field of shape optimization.

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. On the Minimization of Area Among Chord-Convex Sets

    • Beatrice Acciaio, Aldo Pratelli
    Pages 1-17

  3. Optimization Problems Involving the First Dirichlet Eigenvalue and the Torsional Rigidity

    • Michiel van den Berg, Giuseppe Buttazzo, Bozhidar Velichkov
    Pages 19-41

  4. On a Classical Spectral Optimization Problem in Linear Elasticity

    • Davide Buoso, Pier Domenico Lamberti
    Pages 43-55

  5. Metric Spaces of Shapes and Geometries Constructed from Set Parametrized Functions

    • Michel C. Delfour
    Pages 57-101

  6. A Phase Field Approach for Shape and Topology Optimization in Stokes Flow

    • Harald Garcke, Claudia Hecht
    Pages 103-115

  7. An Overview on the Cheeger Problem

    • Gian Paolo Leonardi
    Pages 117-139

  8. Shape- and Topology Optimization for Passive Control of Crack Propagation

    • Günter Leugering, Jan Sokołowski, Antoni Zochowski
    Pages 141-197

  9. Recent Existence Results for Spectral Problems

    • Dario Mazzoleni
    Pages 199-215

  10. Approximate Shape Gradients for Interface Problems

    • A. Paganini
    Pages 217-227

  11. Towards a Lagrange–Newton Approach for PDE Constrained Shape Optimization

    • Volker H. Schulz, Martin Siebenborn, Kathrin Welker
    Pages 229-249

  12. Shape Optimization in Electromagnetic Applications

    • Johannes Semmler, Lukas Pflug, Michael Stingl, Günter Leugering
    Pages 251-269

  13. Shape Differentiability Under Non-linear PDE Constraints

    • Kevin Sturm
    Pages 271-300

  14. Optimal Regularity Results Related to a Partition Problem Involving the Half-Laplacian

    • Alessandro Zilio
    Pages 301-314
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Editors and Affiliations

  • Department Mathematik, Universität Erlangen‐Nürnberg, Erlangen, Germany

    Aldo Pratelli

  • Department Mathematik, Universität Erlangen-Nürnberg, Erlangen, Germany

    Günter Leugering

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Bibliographic Information

  • Book Title: New Trends in Shape Optimization

  • Editors: Aldo Pratelli, Günter Leugering

  • Series Title: International Series of Numerical Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-17563-8

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Hardcover ISBN: 978-3-319-17562-1Published: 08 December 2015

  • Softcover ISBN: 978-3-319-79236-1Published: 21 March 2019

  • eBook ISBN: 978-3-319-17563-8Published: 01 December 2015

  • Series ISSN: 0373-3149

  • Series E-ISSN: 2296-6072

  • Edition Number: 1

  • Number of Pages: VIII, 314

  • Number of Illustrations: 23 b/w illustrations, 29 illustrations in colour

  • Topics: Partial Differential Equations, Systems Theory, Control

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