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An Introduction to Sobolev Spaces and Interpolation Spaces

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Cover of 'An Introduction to Sobolev Spaces and Interpolation Spaces'

Table of Contents

  1. Altmetric Badge
    Book Overview
  2. Altmetric Badge
    Chapter 1 Historical Background
  3. Altmetric Badge
    Chapter 2 The Lebesgue Measure, Convolution
  4. Altmetric Badge
    Chapter 3 Smoothing by Convolution
  5. Altmetric Badge
    Chapter 4 Truncation; Radon Measures; Distributions
  6. Altmetric Badge
    Chapter 5 Sobolev Spaces; Multiplication by Smooth Functions
  7. Altmetric Badge
    Chapter 6 Density of Tensor Products; Consequences
  8. Altmetric Badge
    Chapter 7 Extending the Notion of Support
  9. Altmetric Badge
    Chapter 8 Sobolev's Embedding Theorem, 1 ≤ 
  10. Altmetric Badge
    Chapter 9 Sobolev's Embedding Theorem, N ≤  p  ≤ ∞
  11. Altmetric Badge
    Chapter 10 Poincaramp;#x00E9;'s Inequality
  12. Altmetric Badge
    Chapter 11 The Equivalence Lemma; Compact Embeddings
  13. Altmetric Badge
    Chapter 12 Regularity of the Boundary; Consequences
  14. Altmetric Badge
    Chapter 13 Traces on the Boundary
  15. Altmetric Badge
    Chapter 14 Green's Formula
  16. Altmetric Badge
    Chapter 15 The Fourier Transform
  17. Altmetric Badge
    Chapter 16 Traces of H s ( R N )
  18. Altmetric Badge
    Chapter 17 Proving that a Point is too Small
  19. Altmetric Badge
    Chapter 18 Compact Embeddings
  20. Altmetric Badge
    Chapter 19 Lax–Milgram Lemma
  21. Altmetric Badge
    Chapter 20 The Space H ( div ; Ω )
  22. Altmetric Badge
    Chapter 21 Background on Interpolation; the Complex Method
  23. Altmetric Badge
    Chapter 22 Real Interpolation; K -Method
  24. Altmetric Badge
    Chapter 23 Interpolation of L 2 Spaces with Weights
  25. Altmetric Badge
    Chapter 24 Real Interpolation; J -Method
  26. Altmetric Badge
    Chapter 25 Interpolation Inequalities, the Spaces ( E 0 , E 1 ) θ , 1
  27. Altmetric Badge
    Chapter 26 The Lions–Peetre Reiteration Theorem
  28. Altmetric Badge
    Chapter 27 Maximal Functions
  29. Altmetric Badge
    Chapter 28 Bilinear and Nonlinear Interpolation
  30. Altmetric Badge
    Chapter 29 Obtaining L p by Interpolation, with the Exact Norm
  31. Altmetric Badge
    Chapter 30 My Approach to Sobolev's Embedding Theorem
  32. Altmetric Badge
    Chapter 31 My Generalization of Sobolev's Embedding Theorem
  33. Altmetric Badge
    Chapter 32 Sobolev's Embedding Theorem for Besov Spaces
  34. Altmetric Badge
    Chapter 33 The Lions–Magenes Space $H_{00}^{1/2} ( \Omega)$
  35. Altmetric Badge
    Chapter 34 Defining Sobolev Spaces and Besov Spaces for Ω
  36. Altmetric Badge
    Chapter 35 Characterization of W s , p ( R N )
  37. Altmetric Badge
    Chapter 36 Characterization of W s , p ( Ω )
  38. Altmetric Badge
    Chapter 37 Variants with BV Spaces
  39. Altmetric Badge
    Chapter 38 Replacing BV by Interpolation Spaces
  40. Altmetric Badge
    Chapter 39 Shocks for Quasi-Linear Hyperbolic Systems
  41. Altmetric Badge
    Chapter 40 Interpolation Spaces as Trace Spaces
  42. Altmetric Badge
    Chapter 41 Duality and Compactness for Interpolation Spaces
  43. Altmetric Badge
    Chapter 42 Miscellaneous Questions
  44. Altmetric Badge
    Chapter 43 Biographical Information
  45. Altmetric Badge
    Chapter 44 Abbreviations and Mathematical Notation
Attention for Chapter 11: The Equivalence Lemma; Compact Embeddings
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Chapter title
The Equivalence Lemma; Compact Embeddings
Chapter number 11
Book title
An Introduction to Sobolev Spaces and Interpolation Spaces
Published by
Springer Berlin Heidelberg, November 2015
DOI 10.1007/978-3-540-71483-5_11
Book ISBNs
978-3-54-071482-8, 978-3-54-071483-5
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Mendeley readers

The data shown below were compiled from readership statistics for 1 Mendeley reader of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Unknown 1 100%

Demographic breakdown

Readers by professional status Count As %
Student > Bachelor 1 100%
Readers by discipline Count As %
Mathematics 1 100%