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Local Function Spaces, Heat and Navier-Stokes Equations
Hans Triebel, University of Jena, Germany
A publication of the European Mathematical Society.
EMS Tracts in Mathematics
2013; 241 pp; hardcover
Volume: 20
ISBN-10: 3-03719-123-6
ISBN-13: 978-3-03719-123-1
List Price: US$84
Member Price: US$67.20
Order Code: EMSTM/20
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In this book a new approach is presented to exhibit relations between Sobolev spaces, Besov spaces, and Hölder-Zygmund spaces on the one hand and Morrey-Campanato spaces on the other. Morrey-Campanato spaces extend the notion of functions of bounded mean oscillation. These spaces play an important role in the theory of linear and nonlinear PDEs.

Chapters 1-3 deal with local smoothness spaces in Euclidean \(n\)-space based on the Morrey-Campanato refinement of the Lebesgue spaces. The presented approach relies on wavelet decompositions. This is applied in Chapter 4 to Gagliardo-Nirenberg inequalities. Chapter 5 deals with linear and nonlinear heat equations in global and local function spaces. The obtained assertions about function spaces and nonlinear heat equations are used in Chapter 6 to study Navier-Stokes equations.

The book is addressed to graduate students and mathematicians with a working knowledge of basic elements of (global) function spaces and an interest in applications to nonlinear PDEs with heat and Navier-Stokes equations as prototypes.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.


Graduate students and researchers interested in applications to nonlinear PDEs with heat and Navier-Stokes equations as prototypes.

Table of Contents

  • Global and local spaces
  • Local spaces: Properties
  • Morrey-Campanato spaces
  • Gagliardo-Nirenberg inequalities
  • Heat equations
  • Navier-Stokes equations
  • Bibliography
  • Symbols
  • Index
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