Complementary Variational Principles [2nd ed.] 0198535325, 9780198535324
The book has been mostly rewritten to bring in various improvements and additions. In particular, the local theory is re
299 51 14KB
English Pages C+vii+154+B [166] Year 1980
Table of contents :
Cover
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
Back Cover
Cover
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
Back Cover
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