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Birkhäuser

Inequality Problems in Mechanics and Applications

Convex and Nonconvex Energy Functions

  • Book
  • © 1985

Overview

Authors:
  1. P. D. Panagiotopoulos

    1. Department of Civil Engineering, Aristotle University, Thessaloniki, Greece
      Lehrstuhl und Institut für Technische Mathematik, RWTH Aachen, Aachen, Germany

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xix
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  2. Introductory Topics

    1. Front Matter

      Pages 1-1
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    2. Essential Notions and Propositions of Functional Analysis

      • P. D. Panagiotopoulos
      Pages 3-34

    3. Elements of Convex Analysis

      • P. D. Panagiotopoulos
      Pages 35-60

  3. Inequality Problems

    1. Front Matter

      Pages 61-61
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    2. Variational Inequalities and Superpotentials

      • P. D. Panagiotopoulos
      Pages 63-113

    3. Variational Inequalities and Multivalued Convex and Nonconvex Problems in Mechanics

      • P. D. Panagiotopoulos
      Pages 115-162

    4. Friction Problems in the Theory of Elasticity

      • P. D. Panagiotopoulos
      Pages 163-190

    5. Subdifferential Constitutive Laws and Boundary Conditions

      • P. D. Panagiotopoulos
      Pages 191-213

    6. Inequality Problems in the Theory of Thin Elastic Plates

      • P. D. Panagiotopoulos
      Pages 215-249

    7. Variational and Hemivariational Inequalities in Linear Thermoelasticity

      • P. D. Panagiotopoulos
      Pages 251-275

    8. Variational Inequalities in the Theory of Plasticity and Viscoplasticity

      • P. D. Panagiotopoulos
      Pages 277-320

  4. Numerical Applications

    1. Front Matter

      Pages 321-321
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    2. The Numerical Treatment of Static Inequality Problems

      • P. D. Panagiotopoulos
      Pages 323-347

    3. Incremental and Dynamic Inequality Problems

      • P. D. Panagiotopoulos
      Pages 349-372

  5. Back Matter

    Pages 373-412
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Keywords

About this book

In a remarkably short time, the field of inequality problems has seen considerable development in mathematics and theoretical mechanics. Applied mechanics and the engineering sciences have also benefitted from these developments in that open problems have been treated and entirely new classes of problems have been formulated and solved. This book is an outgrowth of seven years of seminars and courses on inequality problems in mechanics for a variety of audiences in the Technical University of Aachen, the Aristotle University of Thessaloniki, the University of Hamburg and the Technical University of Milan. The book is intended for a variety of readers, mathematicians and engineers alike, as is detailed in the Guidelines for the Reader. It goes without saying that the work of G. Fichera, J. L. Lions, G. Maier, J. J. Moreau in originating and developing the theory of inequality problems has considerably influenced the present book. I also wish to acknowledge the helpful comments received from C. Bisbos, J. Haslinger, B. Kawohl, H. Matthies, H. O. May, D. Talaslidis and B. Werner. Credit is also due to G. Kyriakopoulos and T. Mandopoulou for their exceptionally diligent work in the preparation of the fmal figures. Many thanks are also due to T. Finnegan and J. Gateley for their friendly assistance from the linguistic standpoint. I would also like to thank my editors in Birkhiiuser Verlag for their cooperation, and all those who helped in the preparation of the manuscript.

Authors and Affiliations

  • Department of Civil Engineering, Aristotle University, Thessaloniki, Greece

    P. D. Panagiotopoulos

  • Lehrstuhl und Institut für Technische Mathematik, RWTH Aachen, Aachen, Germany

    P. D. Panagiotopoulos

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