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Regularity Problem for Quasilinear Elliptic and Parabolic Systems

  • Book
  • © 1995

Overview

Authors:
  1. Alexander Koshelev
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1614)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xxi
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  2. Weak solutions and the universal iterative process

    • Alexander Koshelev
    Pages 1-22

  3. Regularity of solutions for non degenerated quasilinear second order elliptic systems of the divergent form with bounded nonlinearities

    • Alexander Koshelev
    Pages 23-71

  4. Some properties and applications of regular solutions for quasilinear elliptic systems

    • Alexander Koshelev
    Pages 72-107

  5. Diffeentiability of solutions for second order elliptic systems

    • Alexander Koshelev
    Pages 108-174

  6. Regularity of solutions for parabolic systems with some applications

    • Alexander Koshelev
    Pages 175-215

  7. The Navier-Stokes system; strong solutions

    • Alexander Koshelev
    Pages 216-247

  8. Back Matter

    Pages 248-255
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Keywords

About this book

The smoothness of solutions for quasilinear systems is one of the most important problems in modern mathematical physics. This book deals with regular or strong solutions for general quasilinear second-order elliptic and parabolic systems. Applications in solid mechanics, hydrodynamics, elasticity and plasticity are described.
The results presented are based on two main ideas: the universal iterative method, and explicit, sometimes sharp, coercivity estimates in weighted spaces. Readers are assumed to have a standard background in analysis and PDEs.

Bibliographic Information

  • Book Title: Regularity Problem for Quasilinear Elliptic and Parabolic Systems

  • Authors: Alexander Koshelev

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0094482

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1995

  • Softcover ISBN: 978-3-540-60251-4Published: 18 September 1995

  • eBook ISBN: 978-3-540-44772-6Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XXII, 262

  • Topics: Analysis

  • Industry Sectors: Energy, Utilities & Environment, Engineering, IT & Software

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