Linear and Quasilinear Parabolic Problems

Volume II: Function Spaces

  • Herbert Amann

Part of the Monographs in Mathematics book series (MMA, volume 106)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Herbert Amann
    Pages 3-73
  3. Herbert Amann
    Pages 75-280
  4. Herbert Amann
    Pages 281-368
  5. Back Matter
    Pages 369-464

About this book


This volume discusses an in-depth theory of function spaces in an Euclidean setting, including several new features, not previously covered in the literature. In particular, it develops a unified theory of anisotropic Besov and Bessel potential spaces on Euclidean corners, with infinite-dimensional Banach spaces as targets.

It especially highlights the most important subclasses of Besov spaces, namely Slobodeckii and Hölder spaces. In this case, no restrictions are imposed on the target spaces, except for reflexivity assumptions in duality results. In this general setting, the author proves sharp embedding, interpolation, and trace theorems, point-wise multiplier results, as well as Gagliardo-Nirenberg estimates and generalizations of Aubin-Lions compactness theorems.

The results presented pave the way for new applications in situations where infinite-dimensional target spaces are relevant – in the realm of stochastic differential equations, for example.


Linear Theory Function Spaces Linear and Quasilinear Parabolic Problems Sequence Spaces Anisotropy Besov Spaces

Authors and affiliations

  • Herbert Amann
    • 1
  1. 1.Institut für MathematikUniversität of ZürichZürichSwitzerland

Bibliographic information