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Optimization of Elliptic Systems

Theory and Applications

  • Book
  • © 2006

Overview

Authors:
  1. Pekka Neittaanmaki

    1. Department of Mathematical, Information Technology, University of Jyvaskyla, Jyvaskyla, Finland
      Department of Mathematics and Statistics, University of Jyvaskyla, Jyvaskyla, Finland

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  2. Dan Tiba

    1. Institute of Mathematics, Romanian Academy, Bucuresti

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  3. Jürgen Sprekels

    1. Angew. Analysis und Stochastik Abt. Part. Differentialgleichg, Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

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  • Provides a comprehensive and accessible introduction to the optimization of elliptic systems
  • The authors clarify connections between seemingly disparate types of problems
  • Organized to impart a gradual and accessible presentation of the material, using numerous examples
  • Useful for graduate students and researchers in the field of elliptic systems, and for scientists in physics, mechanics, and engineering

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xv
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  2. Introductory Topics

    Pages 1-23

  3. Existence

    Pages 25-82

  4. Optimality Conditions

    Pages 83-191

  5. Discretization

    Pages 193-248

  6. Unknown Domains

    Pages 249-339

  7. Optimization of Curved Mechanical Systems

    Pages 341-435

  8. Back Matter

    Pages 437-507
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Keywords

About this book

The present monograph is intended to provide a comprehensive and accessible introduction to the optimization of elliptic systems. This area of mathematical research, which has many important applications in science and technology. has experienced an impressive development during the past two decades. There are already many good textbooks dealing with various aspects of optimal design problems. In this regard, we refer to the works of Pironneau [1984], Haslinger and Neittaanmaki [1988], [1996], Sokolowski and Zolksio [1992], Litvinov [2000], Allaire [2001], Mohammadi and Pironneau [2001], Delfour and Zolksio [2001], and Makinen and Haslinger [2003]. Already Lions [I9681 devoted a major part of his classical monograph on the optimal control of partial differential equations to the optimization of elliptic systems. Let us also mention that even the very first known problem of the calculus of variations, the brachistochrone studied by Bernoulli back in 1696. is in fact a shape optimization problem. The natural richness of this mathematical research subject, as well as the extremely large field of possible applications, has created the unusual situation that although many important results and methods have already been est- lished, there are still pressing unsolved questions. In this monograph, we aim to address some of these open problems; as a consequence, there is only a minor overlap with the textbooks already existing in the field.

Reviews

From the reviews:

"The book gives a comprehensive view of the optimization of systems governed by partial differential equations of elliptic type. … The book is carefully written. Basic tools of convex analysis, an abstract optimization theory, notions on the well-posedness of elliptic systems, and the existence results for optimal control problems are presented in a simple way. … The book will therefore be useful for confirmed researchers as well as students willing to enter in the field. One could even teach a graduate course by selecting material." (Joseph Frédéric Bonnans, Zentralblatt MATH, Vol. 1106 (8), 2007)

Authors and Affiliations

  • Department of Mathematical, Information Technology, University of Jyvaskyla, Jyvaskyla, Finland

    Pekka Neittaanmaki

  • Department of Mathematics and Statistics, University of Jyvaskyla, Jyvaskyla, Finland

    Pekka Neittaanmaki

  • Institute of Mathematics, Romanian Academy, Bucuresti

    Dan Tiba

  • Angew. Analysis und Stochastik Abt. Part. Differentialgleichg, Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Jürgen Sprekels

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