An Introduction to Sobolev Spaces and Interpolation Spaces

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ISBN: 978-3-540-71482-8 (Print) 978-3-540-71483-5 (Online)

Table of contents (44 chapters)

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  1. Front Matter

    Pages I-XXV

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    Pages 1-7

    Historical Background

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    Pages 9-14

    The Lebesgue Measure, Convolution

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    Pages 15-16

    Smoothing by Convolution

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    Pages 17-20

    Truncation; Radon Measures; Distributions

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    Pages 21-25

    Sobolev Spaces; Multiplication by Smooth Functions

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    Pages 27-31

    Density of Tensor Products; Consequences

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    Pages 33-36

    Extending the Notion of Support

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    Pages 37-41

    Sobolev's Embedding Theorem, 1 ≤ < N

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    Pages 43-47

    Sobolev's Embedding Theorem, N ≤ p ≤ ∞

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    Pages 49-51

    Poincaramp;#x00E9;'s Inequality

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    Pages 53-57

    The Equivalence Lemma; Compact Embeddings

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    Pages 59-63

    Regularity of the Boundary; Consequences

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    Pages 65-68

    Traces on the Boundary

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    Pages 69-71

    Green's Formula

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    Pages 73-79

    The Fourier Transform

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    Pages 81-84

    Traces of H s (R N )

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    Pages 85-87

    Proving that a Point is too Small

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    Pages 89-92

    Compact Embeddings

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    Pages 93-98

    Lax–Milgram Lemma

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    Pages 99-101

    The Space H(div;Ω)

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