2011 | OriginalPaper | Buchkapitel
Introduction to Sobolev Spaces
verfasst von : Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Růžička
Erschienen in: Lebesgue and Sobolev Spaces with Variable Exponents
Verlag: Springer Berlin Heidelberg
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In this chapter we begin our study of Sobolev functions. The Sobolev space is a vector space of functions with weak derivatives. One motivation of studying these spaces is that solutions of partial differential equations belong naturally to Sobolev spaces (cf. Part III). In Sect. 8.1 we study functional analysis-type properties of Sobolev spaces, in particular we show that the Sobolev space is a Banach space and study its basic properties as reflexivity, separability and uniform convexity.