UID:
almafu_9958120100602883
Umfang:
1 online resource (329 p.)
ISBN:
1-281-76651-8
,
9786611766511
,
0-08-087404-5
Serie:
Pure and applied mathematics (Academic Press) ; 88
Inhalt:
An introduction to variational inequalities and their applications
Anmerkung:
Description based upon print version of record.
,
Front Cover; An Introduction to Variational Inequalities and Their Applications; Copyright Page; Contents; Preface; Glossary of Notations; Introduction; Chapter I. Variational Inequalities in Rn; 1. Fixed Points; 2. The Characterization of the Projection onto a Convex Set; 3. A First Theorem about Variational Inequalities; 4. Variational Inequalities; 5. Some Problem Which Lead to Variational Inequalities; Comments and Bibliographical Notes; Exercises; Chapter II. Variational Inequalities in Hilbert Space; 1. Bilinear Forms; 2. Existence of a Solution; 3. Truncation
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4. Sobolev Spaces and Boundary Value Problems5. The Weak Maximum Principle; 6. The Obstacle Problem: First Properties; 7. The Obstacle Problem in the One Dimensional Case; Appendix A. Sobolev Spaces; Appendix B. Solutions to Equations with Bounded Measurable Coefficients; Appendix C. Local Estimates of Solutions; Appendix D. Hölder Continuity of the Solutions; Comments and Bibliographical Notes; Exercises; Chapter III. Variational Inequalities for Monotone Operators; 1. An Abstract Existence Theorem; 2. Noncoercive Operators; 3. Semilinear Equations; 4. Quasi-Linear Operators
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Comments and Bibliographical NotesExercises; Chapter IV. Problems of Regularity; 1. Penalization; 2. Dirichlet Integral; 3. Coercive Vector Fields; 4. Locally Coercive Vector Fields; 5. Another Penalization; 6. Limitation of Second Derivatives; 7. Bounded Variation of Au; 8. Lipschitz Obstacles; 9. A Variational Inequality with Mixed Boundary Conditions; Appendix A. Proof of Theorem 3.3; Comments and Bibliographical Notes; Exercises; Chapter V. Free Boundary Problems and the Coincidence Set of the Solution; I. Introduction; 2. The Hodograph and Legendre Transformations
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3. The Free Boundary in Two Dimensions4. A Remark about Singularities; 5. The Obstacle Problem for a Minimal Surface; 6. The Topology of the Coincidence Set When the Obstacle Is Concave; 7. A Remark about the Coincidence Set in Higher Dimensions; Comments and Bibliographical Notes; Exercises; Chapter VI. Free Boundary Problems Governed by Elliptic Equations and Systems; I. Introduction; 2. Hodograph and Legendre Transforms: The Theory of a Single Equation; 3. Elliptic Systems; 4. A Reflection Problem; 5. Elliptic Equations Sharing Cauchy Data; 6. A Problem of Two Membranes
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Comments and Bibliographical NotesExercises; Chapter VII. Applications of Variational Inequalities; 1. Introduction; 2. A Problem in the Theory of Lubrication; 3. The Filtration of a Liquid through a Porous Medium; 4. The Resolution of the Filtration Problem by Variational Inequalities; 5. The Filtration of a Liquid through a Porous Medium with Variable Cross Section; 6. The Resolution of the Filtration Problem in Three Dimensions; 7. Flow past a Given Profile: The Problem in the Physical Plane; 8. Flow past a Given Profile: Resolution by Variational Inequalities
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9. The Deflection of a Simply Supported Beam
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English
Weitere Ausg.:
ISBN 0-12-407350-6
Sprache:
Englisch
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