Obstacle Problems in Mathematical PhysicsElsevier, 01.03.1987 - 351 Seiten 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 the free boundary and including some results on the obstacle Plateau problem. The last part examines the application to free boundary problems, namely the lubrication-cavitation problem, the elastoplastic problem, the Signorini (or the boundary obstacle) problem, the dam problem, the continuous casting problem, the electrochemical machining problem and the problem of the flow with wake in a channel past a profile. |
Inhalt
| 1 | |
| 22 | |
Chapter 3 Some Mathematical Tools | 54 |
Chapter 4 Variational Inequalities in Hilbert Spaces | 87 |
Chapter 5 Smoothness of the Variational Solution | 136 |
Chapter 6 The Coincidence Set and the Free Boundary | 185 |
Chapter 7 Unilateral Plateau Problems | 227 |
Chapter 8 Applied Obstacle Problems | 251 |
Chapter 9 Dam and Stefan Type Problems | 289 |
| 329 | |
| 349 | |
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Häufige Begriffe und Wortgruppen
a.e. in Q analytic apply arbitrary Assume assumptions Banach space boundary conditions boundary value problem bounded coefficients coercive coincidence set compact concludes consequence consider constant convergence convex set corresponding dam problem defined denotes Dirichlet Dirichlet problem domain elliptic equation equivalent estimate exists finite follows easily free boundary problems function g on 30 given Green's formula Hausdorff distance Hence Hilbert space Hölder continuity holds implies Lebesgue Lemma Let Q linear Lions-Stampacchia theorem Lipschitz Lipschitz domains LP(Q maximum principle mean curvature minimal surface monotone Neumann nonlinear nonnegative norm obstacle problem obtains open set operator Proposition recall regularity REMARK resp Section sequence smooth ſº solves Stampacchia Stefan problem subset supersolution Theorem 3.1 theory topology unique solution variational inequality vector verifying
Verweise auf dieses Buch
KKM Theory and Applications in Nonlinear Analysis George Xian-Zhi Yuan Eingeschränkte Leseprobe - 1999 |