Abstract
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.
Keywords
- Sobolev Space
- Extension Operator
- Sobolev Embedding
- Variable Exponent
- Riesz Potential
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© 2011 Springer-Verlag Berlin Heidelberg
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Diening, L., Harjulehto, P., Hästö, P., Růžička, M. (2011). Introduction to Sobolev Spaces. In: Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics(), vol 2017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18363-8_8
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DOI: https://doi.org/10.1007/978-3-642-18363-8_8
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-18362-1
Online ISBN: 978-3-642-18363-8
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