Abstract
This chapter is concerned with the fundamental properties of Sobolev spaces including the Sobolev inequality and its associated imbedding theorems. The basic Sobolev inequality is proved in two ways, one of which employs the co-area formula (Section 2.7) to obtain the best constant in the inequality. This method relates the Sobolev inequality to the isoperimetric inequality.
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© 1989 Springer Science+Business Media New York
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Ziemer, W.P. (1989). Sobolev Spaces and Their Basic Properties. In: Weakly Differentiable Functions. Graduate Texts in Mathematics, vol 120. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1015-3_2
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DOI: https://doi.org/10.1007/978-1-4612-1015-3_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6985-4
Online ISBN: 978-1-4612-1015-3
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