Optimization of Elliptic Systems (eBook)

Theory and Applications

Pekka Neittaanmaki, Jürgen Sprekels, Dan Tiba (Autoren)

eBook Download: PDF

2007 | 1. Auflage
512 Seiten
Springer-Verlag
978-0-387-27236-8 (ISBN)

Infos

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.

Inhalt

Preface 5
A Brief Reader's Guide 11
Contents 12
Chapter 1 Introductory Topics 15
Chapter 2 Existence 38
Chapter 3 Optimality Conditions 96
Chapter 4 Discretization 205
Chapter 5 Unknown Domains 261
Chapter 6 Optimization of Curved Mechanical Systems 352
Appendix 1 Convex Mappings and Monotone Operators 447
Appendix 2 Elliptic Equations and Variational Inequalities 460
Appendix 3 Domain Convergence 468
Bibliography 483
Index 502
Notation 512

Produkt-Details

• Erscheint lt. Verlag: 4.1.2007
• Reihe/Serie: Springer Monographs in Mathematics
• Reihe/Serie: Springer Monographs in Mathematics
• Zusatzinfo: XVI, 512 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: Development • Equation • Mathematics • Mechanics • Optimization • Partial differential equations • Physics • Science • Technology • Variable
• ISBN-10: 0-387-27236-4 / 0387272364
• ISBN-13: 978-0-387-27236-8 / 9780387272368