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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.

Mathematical physics

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Architectural design --- Architecture --- Design architectural --- Congresses. --- Mathematics --- Congrès --- Mathématiques --- 72.012/013 --- 51 --- Gulden snede (architectuur) --- Modulaire coordinatie --- Proportie (architectuur) --- Symmetrie (architectuur) --- Wiskunde --- Mathematica --- Congrès --- Mathématiques

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This book is the “Study Book” of ICMI-Study no. 20, which was run in cooperation with the International Council for Industry and Applied Mathematics (ICIAM). The editors were the co-chairs of the study (Damlamian, Straesser) and the organizer of the Study Conference (Rodrigues). The text contains a comprehensive report on the findings of the Study Conference, original plenary presentations of the Study Conference, reports on the Working Groups and selected papers from all over the world. This content was selected by the editors as especially pertinent to the study, each individual chapter representing a significant contribution to current research. .

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