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Theses (Scuola Normale Superiore)

Existence and Regularity Results for Some Shape Optimization Problems

Authors: Velichkov, Bozhidar

  • ​Provides a detailed and self-contained introduction to the recent results and techniques in shape optimization
  • Presents new techniques concerning the regularity of the optimal sets
  • Self-contained exposition requiring only basic knowledge of Sobolev spaces and BV functions
  • Includes a self-contained and simplified introduction to the existence theory introduced by Buttazzo and Dal Maso in the 90s  
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eBook $19.99
price for USA (gross)
  • ISBN 978-88-7642-527-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $24.99
price for USA
  • ISBN 978-88-7642-526-4
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
About this book

​We study the existence and regularity of optimal domains for functionals depending on the spectrum of the Dirichlet Laplacian or of more general Schrödinger operators. The domains are subject to perimeter and volume constraints; we also take into account the possible presence of geometric obstacles. We investigate the properties of the optimal sets and of the optimal state functions. In particular, we prove that the eigenfunctions are Lipschitz continuous up to the boundary and that the optimal sets subject to the perimeter constraint have regular free boundary. We also consider spectral optimization problems in non-Euclidean settings and optimization problems for potentials and measures, as well as multiphase and optimal partition problems. 

Table of contents (7 chapters)

  • Introduction and Examples

    Velichkov, Bozhidar

    Pages 1-12

  • Shape optimization problems in a box

    Velichkov, Bozhidar

    Pages 13-58

  • Capacitary measures

    Velichkov, Bozhidar

    Pages 59-136

  • Subsolutions of shape functionals

    Velichkov, Bozhidar

    Pages 137-201

  • Shape supersolutions and quasi-minimizers

    Velichkov, Bozhidar

    Pages 203-257

Buy this book

eBook $19.99
price for USA (gross)
  • ISBN 978-88-7642-527-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $24.99
price for USA
  • ISBN 978-88-7642-526-4
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
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Bibliographic Information

Bibliographic Information
Book Title
Existence and Regularity Results for Some Shape Optimization Problems
Authors
Series Title
Theses (Scuola Normale Superiore)
Series Volume
19
Copyright
2015
Publisher
Edizioni della Normale
Copyright Holder
Scuola Normale Superiore Pisa
eBook ISBN
978-88-7642-527-1
DOI
10.1007/978-88-7642-527-1
Softcover ISBN
978-88-7642-526-4
Edition Number
1
Number of Pages
XVI, 349
Topics