Sobolev Spaces

with Applications to Elliptic Partial Differential Equations

Authors:

ISBN: 978-3-642-15563-5 (Print) 978-3-642-15564-2 (Online)

Table of contents (18 chapters)

  1. Front Matter

    Pages I-XXVIII

  2. No Access

    Book Chapter

    Pages 1-121

    Basic Properties of Sobolev Spaces

  3. No Access

    Book Chapter

    Pages 123-229

    Inequalities for Functions Vanishing at the Boundary

  4. No Access

    Book Chapter

    Pages 231-253

    Conductor and Capacitary Inequalities with Applications to Sobolev-Type Embeddings

  5. No Access

    Book Chapter

    Pages 255-286

    Generalizations for Functions on Manifolds and Topological Spaces

  6. No Access

    Book Chapter

    Pages 287-321

    Integrability of Functions in the Space $L^{1}_{1}(\varOmega )$

  7. No Access

    Book Chapter

    Pages 323-404

    Integrability of Functions in the Space $L^{1}_{p}(\varOmega )$

  8. No Access

    Book Chapter

    Pages 405-434

    Continuity and Boundedness of Functions in Sobolev Spaces

  9. No Access

    Book Chapter

    Pages 435-458

    Localization Moduli of Sobolev Embeddings for General Domains

  10. No Access

    Book Chapter

    Pages 459-509

    Space of Functions of Bounded Variation

  11. No Access

    Book Chapter

    Pages 511-548

    Certain Function Spaces, Capacities, and Potentials

  12. No Access

    Book Chapter

    Pages 549-609

    Capacitary and Trace Inequalities for Functions in ℝ n with Derivatives of an Arbitrary Order

  13. No Access

    Book Chapter

    Pages 611-655

    Pointwise Interpolation Inequalities for Derivatives and Potentials

  14. No Access

    Book Chapter

    Pages 657-668

    A Variant of Capacity

  15. No Access

    Book Chapter

    Pages 669-692

    Integral Inequality for Functions on a Cube

  16. No Access

    Book Chapter

    Pages 693-735

    Embedding of the Space $\mathaccent"7017{L}^{l}_{p}(\varOmega)$ into Other Function Spaces

  17. No Access

    Book Chapter

    Pages 737-753

    Embedding $\mathaccent "7017{L}^{l}_{p}(\varOmega, \nu) \subset W^{m}_{r}(\varOmega)$

  18. No Access

    Book Chapter

    Pages 755-768

    Approximation in Weighted Sobolev Spaces

  19. No Access

    Book Chapter

    Pages 769-801

    Spectrum of the Schrödinger Operator and the Dirichlet Laplacian

  20. Back Matter

    Pages 803-866