Abstract
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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© 1985 Birkhäuser Boston Inc.
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Panagiotopoulos, P.D. (1985). Essential Notions and Propositions of Functional Analysis. In: Inequality Problems in Mechanics and Applications. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-5152-1_1
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DOI: https://doi.org/10.1007/978-1-4612-5152-1_1
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3094-2
Online ISBN: 978-1-4612-5152-1
eBook Packages: Springer Book Archive