Descript 
ix, 232 pages : illustration ; 25 cm 

text rdacontent 

unmediated rdamedia 

volume rdacarrier 
Series 
EMS tracts in mathematics ; 20 

EMS tracts in mathematics ; 20

Note 
Includes bibliographical references (pages 215227) and index 

1. Global and local spaces  2. Local spaces: properties  3. MorreyCampanato spaces  4. GaliardoNirenberg inequalities  5. Heat equations  6, NavierStokes equations 

In this book a new approach is presented to exhibit relations between Sobolev spaces, Besov spaces, and HölderZygmund spaces on the one hand and MorreyCampanato spaces on the other. MorreyCampanato 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 13 deal with local smoothness spaces in Euclidean nspace based on the MorreyCampanato refinement of the Lebesgue spaces. The presented approach relies on wavelet decompositions. This is applied in Chapter 4 to GagliardoNirenberg 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 NavierStokes equations. The book is addressed to graduate students and mathematicians having a working knowledge of basic elements of (global) function spaces, and who are interested in applications to nonlinear PDEs with heat and NavierStokes equations as prototypes 
Subject 
Function spaces


Heat equation


NavierStokes equations

