Abstract
This chapter reviews two types of results on the Sobolev spaces introduced in the previous chapter. The first one concerns the notion of trace (loosely speaking, the boundary values) of functions in Sobolev spaces. The second one is about functional inequalities due to Poincaré and Steklov. The validity of some of these results relies on smoothness properties of the boundary of the set on which the functions are defined. We mainly focus on Lipschitz sets in this book.
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Ern, A., Guermond, JL. (2021). Traces and Poincaré inequalities. In: Finite Elements I. Texts in Applied Mathematics, vol 72. Springer, Cham. https://doi.org/10.1007/978-3-030-56341-7_3
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DOI: https://doi.org/10.1007/978-3-030-56341-7_3
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Online ISBN: 978-3-030-56341-7
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