Overview
- Shape optimization problems are treated from the classical and modern perspectives
- Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems
- Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis
- Driven by several good examples and illustrations
- Poses some open questions
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 65)
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Table of contents(7 chapters)
About this book
Reviews
From the reviews:
"The book under review deals with some variational methods to treat shape optimization problems … . The book contains a complete study of mathematical problems for scalar equations and eigenvalues, in particular regarding the existence of solutions in shape optimization. … The main goal of the book is to focus on the existence of an optimal shape, necessary conditions of optimality, and stability of optimal solutions under some prescribed kind of perturbations." (Jan Sokolowski, Mathematical Reviews, Issue 2006 j)
“The authors predominantly analyze optimal shape and optimal control problems … . The book, though slim, is rich in content and provides the reader with a wealth of information, numerous analysis and proof techniques, as well as useful references (197 items). … Numerous nontrivial examples illustrate the theory and can please even those readers who are rather application-oriented.” (Jan Chleboun, Applications of Mathematics, Vol. 55 (5), 2010)
Authors and Affiliations
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Département de Mathématiques, Université de Metz, Metz Cedex 01, France
Dorin Bucur
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Dipartimento di Matematica, Università di Pisa, Pisa, Italy
Giuseppe Buttazzo
Bibliographic Information
Book Title: Variational Methods in Shape Optimization Problems
Authors: Dorin Bucur, Giuseppe Buttazzo
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/b137163
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2005
Hardcover ISBN: 978-0-8176-4359-1
eBook ISBN: 978-0-8176-4403-1
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 1
Number of Pages: VIII, 216
Topics: Calculus of Variations and Optimal Control; Optimization, Optimization, Partial Differential Equations, Functional Analysis, Difference and Functional Equations, Applications of Mathematics