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Published in:
1994 | OriginalPaper | Chapter
Sobolev Spaces
Authors : Susanne C. Brenner, L. Ridgway Scott
Published in: The Mathematical Theory of Finite Element Methods
Publisher: Springer New York
Included in: Professional Book Archive
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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.