TL;DRAbstract
The aim of Chapter 1 is to provide some notions and propositions of functional analysis which will be necessary in the next chapters for the study of inequality problems in mechanics. Commencing with the notion of topological vector spaces and the corresponding notion of duality, we give some properties of certain function spaces. Particular attention is paid to Sobolev spaces and spaces of functions of bounded deformation for which the trace theorems and some imbedding properties are given. Korn’s inequalities and the Green-Gauss theorem are also presented. Elements of the theory of vector-valued functions and distributions as well as of differential calculus close this chapter.
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The aim of Chapter 1 is to provide some notions and propositions of functional analysis which will be necessary in the next chapters for the study of inequality problems in mechanics. Commencing with the notion of topological vector spaces and the corresponding notion of duality, we give some properties of certain function spaces. Particular attention is paid to Sobolev spaces and spaces of functions of bounded deformation for which the trace theorems and some imbedding properties are given. Korn’s inequalities and the Green-Gauss theorem are also presented. Elements of the theory of vector-valued functions and distributions as well as of differential calculus close this chapter.
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