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Sobolev Spaces

  • Textbook
  • © 1985

Overview

Authors:
  1. Vladimir G. Maz’ja

    1. Faculty of Mathematics and Mechanics, Leningrad University, Leningrad, USSR

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Part of the book series: Springer Series in Soviet Mathematics (SSSOV)

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-XIX
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  2. Introduction

    • Vladimir G. Maz’ja
    Pages 1-5

  3. Basic Properties of Sobolev Spaces

    • Vladimir G. Maz’ja
    Pages 6-87

  4. Inequalities for Gradients of Functions that Vanish on the Boundary

    • Vladimir G. Maz’ja
    Pages 88-159

  5. On Summability of Functions in the Space L 11 (Ω)

    • Vladimir G. Maz’ja
    Pages 160-190

  6. On Summability of Functions in the Space L 1 p (Ω)

    • Vladimir G. Maz’ja
    Pages 191-269

  7. On Continuity and Boundedness of Functions in Sobolev Spaces

    • Vladimir G. Maz’ja
    Pages 270-295

  8. On Functions in the Space B V(Ω)

    • Vladimir G. Maz’ja
    Pages 296-341

  9. Certain Function Spaces, Capacities and Potentials

    • Vladimir G. Maz’ja
    Pages 342-359

  10. On Summability with Respect to an Arbitrary Measure of Functions with Fractional Derivatives

    • Vladimir G. Maz’ja
    Pages 360-389

  11. A Variant of Capacity

    • Vladimir G. Maz’ja
    Pages 390-401

  12. An Integral Inequality for Functions on a Cube

    • Vladimir G. Maz’ja
    Pages 402-423

  13. Imbedding of the Space into Other Function Spaces

    • Vladimir G. Maz’ja
    Pages 424-452

  14. The Imbedding

    • Vladimir G. Maz’ja
    Pages 453-468

  15. Back Matter

    Pages 469-488
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Keywords

About this book

The Sobolev spaces, i. e. the classes of functions with derivatives in L , occupy p an outstanding place in analysis. During the last two decades a substantial contribution to the study of these spaces has been made; so now solutions to many important problems connected with them are known. In the present monograph we consider various aspects of Sobolev space theory. Attention is paid mainly to the so called imbedding theorems. Such theorems, originally established by S. L. Sobolev in the 1930s, proved to be a useful tool in functional analysis and in the theory of linear and nonlinear par­ tial differential equations. We list some questions considered in this book. 1. What are the requirements on the measure f1, for the inequality q

Authors and Affiliations

  • Faculty of Mathematics and Mechanics, Leningrad University, Leningrad, USSR

    Vladimir G. Maz’ja

Bibliographic Information

  • Book Title: Sobolev Spaces

  • Authors: Vladimir G. Maz’ja

  • Series Title: Springer Series in Soviet Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-09922-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1985

  • eBook ISBN: 978-3-662-09922-3Published: 21 December 2013

  • Series ISSN: 0939-1169

  • Edition Number: 1

  • Number of Pages: XIX, 488

  • Topics: Analysis

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