Complementary Variational Principles [2nd ed.] 0198535325, 9780198535324

Table of contents :
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OXFORD MATHEMATICAL MONOGRAPHS


COMPLEMENTARY VARIATIONAL PRINCIPLES


Copyright

Oxford University Press 1980

ISBN 0-19-853532-5

515'.62 QA379

LCCN 80-0613


PREFACE


CONTENTS


1 VARIATIONAL PRINCIPLES: INTRODUCTION

1.1. Introduction

1.2. Euler-Lagrange theory

1.3. Canonical formalism

1.4 Convex functions

1.5. Complementary variational principles


2 VARIATIONAL PRINCIPLES: SOME EXTENSIONS

2.1. A class of operators

2.2. Functional derivatives

2.3. Euler-Lagrange theory

2.4. Canonical formalism

2.5. Convex functionals

2.6. Complementary variational principles


3 LINEAR BOUNDARY-VALUE PROBLEMS

3.1. The inverse problem

3.2. A lass of linear problems

3.3. Variational formulation

3.4. Complementary principles

3.5. The hypercirde

3.6. Error estimates for approximate solutions

3.7. Alternative complementary principles

3.8. Estes for linear functionals


4 LINEAR APPLICATIONS

4.1. The Rayleigh and Temple bounds

4.2. Potential theory

4.3. Electrostatics

4.4. Diffusion

4.5. The Mime problem

4.6. Membrane with elastic support

4.7. Perturbation theory

4.8. Potential scattering

4.9. Other applications


5 NONLINEAR BOUNDARY-VALUE PROBLEMS

5.1. Class of problems

5.2. Variational formulation

5.3. Complementary principles

5.4. Monotone problems

5.5. Error estimates

5.6. Hypercircle results for monotone problems

5.7. Geometry of the general problem

5.8. Estimates for linear functionals


6 NONLINEAR APPLICATIONS

6.1. Poisson-Boltzmann equation

6.2. 17wmas.-Fermi equation

6.3. F8pp1-Henclcy equation

6.4. Prismatic bar

6.5. An integrral equation

6.6. Nonlinear diffusion

6.7. Nerve membrane problem

6.8. Nonlinear networks

6.9. Other applications

Conduding remarks



REFERENCES


SUBJECT INDEX


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