UID:
almahu_9949698018202882
Format:
1 online resource (369 p.)
ISBN:
1-281-79799-5
,
9786611797997
,
0-08-087245-X
Series Statement:
North-Holland mathematics studies ; 134
Content:
The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics.The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of
Note:
Description based upon print version of record.
,
Front Cover; Obstacle Problems in Mathematical Physics; Copyright Page; Contents; Preface; Acknowledgments; Notations; Chapter 1. The Obstacle Problem; 1. Introduction; 2. Deformation of a Membrane Constrained by an Obstacle; 3. Discussion of the Variational Inequality Formulation; 4. Bending of a Plate over an Obstacle; 5. Minimal and Capillary Surfaces with Obstacles; 6. The Elastoplastic Torsion of a Cylindrical Bar; 7. A Cavitation Problem in Hydrodynamic Lubrication; 8. Mixed and Boundary Obstacle Problems; 9. Comments; Chapter 2. Some Free Boundary Problems; 1. Introduction
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2. Conservation Laws in Continuum Physics3. Filtration through a Porous Medium; 4. The Baiocchi Transformation for the Dam Problem; 5. Solidification of a Continuous Ingot; 6. Continuous Casting by Variational Inequalities; 7. Quasi-Steady Electrochemical Shaping; 8. The Transformed ECM Problem; 9. On the Applicability of Variational Inequalities; 10. Flow with Wake in a Channel past a Profile; 11. The One Phase Stefan Problem; 12. Comments; Chapter 3. Some Mathematical Tools; 1. Introduction; 2. Basic Functional Analysis; 3. Functions Spaces; 4. Lipschitz Domains of Rn
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5. Traces and Imbedding Theorems6. Green's Formula and Boundary Value Problems; 7. Second Order Elliptic Equations; 8. Comments; Chapter 4. Variational Inequalities in Hilbert Spaces; 1. Introduction; 2. The Projection Theorem; 3. The Lions-Stampacchia Theorem; 4. Abstract Stability Results; 5. Positivity, Comparison and Maximum Principles; 6. The Semi-Linear Mixed Obstacle Problem; 7. The Case of Noncoercive Bilinear Form; 8. Quasi-Linear Obstacle Problems; 9. Singular Perturbations in Variational Inequalities; 10. Comments; Chapter 5. Smoothness of the Variational Solution; 1. Introduction
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2. Dual Estimates and Regularity3. A Penalization for the Obstacle Problem; 4. Strong Continuous Dependence; 5 . Boundary Penalization and Localization; 6. Boundedness of Second Derivatives; 7. Hölder Continuity of the Solution; 8. Relations with Potential Theory; 9. Comments; Chapter 6. The Coincidence Set and the Free Boundary; 1. Introduction; 2. Bidimensional Free Boundaries; 3. Caffarelli's Theorem and General Regularity; 4. Cylindrical, Starshaped and Convex Configurations; 5. Stability of the Free Boundary; 6. General Stability Conditions; 7. Estimates on the Coincidence Set
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8. Further Remarks on the Free Boundary9. Comments; Chapter 7. Unilateral Plateau Problems; 1. Introduction; 2. Surfaces of Constant Mean Curvature with Obstacles; 3. Continuous Dependence on the Domain and on the Obstacle; 4. Smoothness of H-Surfaces over Obstacles; 5. Some Properties of the Free Boundary; 6. Comments; Chapter 8. Applied Obstacle Problems; 1. Introduction; 2. Asymptotic Analysis in the Lubrication Problem; 3. The Lubrication Problem with Small Eccentricity; 4. The Elastoplastic Variational Inequality; 5. The Elastoplastic Free Boundary; 6. The Signorini Problem
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7. Remarks on the Thin Obstacle Problem
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English
Additional Edition:
ISBN 0-444-70187-7
Language:
English
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