Obstacle Problems in Mathematical Physics


  • J.-F. Rodrigues

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.
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Book information

  • Published: March 1987
  • Imprint: NORTH-HOLLAND
  • ISBN: 978-0-444-70187-9

Table of Contents

I. A Mathematical Physics Introduction. The Obstacle Problem. Some Free Boundary Problems. Some Mathematical Tools. II. Unilateral Elliptic Variational Inequalities. Variational Inequalities in Hilbert Spaces. Smoothness of the Variational Solution. The Coincidence Set and the Free Boundary. Unilateral Plateau Problems. III. Applications in Mechanics and in Physics. Applied Obstacle Problems. Dam and Stefan Type Problems. Bibliography. Index.