Abstract
This chapter is devoted to developing function spaces that are used in the variational formulation of differential equations. We begin with a review of Lebesgue integration theory, upon which our notion of “variational” or “weak” derivative rests. Functions with such “generalized” derivatives make up the spaces commonly referred to as Sobolev spaces. We develop only a small fraction of the known theory for these spaces — just enough to establish a foundation for the finite element method.
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© 2002 Springer Science+Business Media New York
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Brenner, S.C., Scott, L.R. (2002). Sobolev Spaces. In: The Mathematical Theory of Finite Element Methods. Texts in Applied Mathematics, vol 15. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3658-8_2
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DOI: https://doi.org/10.1007/978-1-4757-3658-8_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-3660-1
Online ISBN: 978-1-4757-3658-8
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