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Variable Lebesgue Spaces pp 239–270Cite as

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Basic Properties of Variable Sobolev Spaces

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Abstract

In this chapter we present the elementary theory of variable Sobolev spaces. Unlike Chap. 2, where we systematically developed a complete theory of variable Lebesgue spaces, our goal here is less ambitious. Our aim is to illustrate how the theorems and techniques given in previous chapters can be applied to the variable Sobolev spaces. Consequently, many of our results are not given in the fullest generality possible, and there are a number of results from the classical theory of Sobolev spaces that we do not discuss.

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Authors and Affiliations

  1. Department of Mathematics, Trinity College, Hartford, Connecticut, USA

    David V. Cruz-Uribe

  2. Dipartimento di Architettura, Università di Napoli “Federico II”, Napoli, Italy

    Alberto Fiorenza

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  1. David V. Cruz-Uribe
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Cruz-Uribe, D.V., Fiorenza, A. (2013). Basic Properties of Variable Sobolev Spaces. In: Variable Lebesgue Spaces. Applied and Numerical Harmonic Analysis. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0548-3_6

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