02705nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185100002800221245010000249260008200349300003400431336002600465337002600491338003600517347002400553490004000577506006600617520138900683650003502072650002902107650004002136650002602176650002802202856003202230856006902262185-150120CH-001817-320150120234500.0a fot ||| 0|cr nn mmmmamaa150120e20150115sz fot ||| 0|eng d a978303719650270a10.4171/1502doi ach0018173 7aPBKJ2bicssc a46-xxa35-xxa42-xxa45-xx2msc1 aTriebel, Hans,eauthor.10aHybrid Function Spaces, Heat and Navier-Stokes Equationsh[electronic resource] /cHans Triebel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2015 a1 online resource (196 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v241 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book is the continuation of Local Function Spaces, Heat and Navier–Stokes Equations (Tracts in Mathematics 20, 2013) by the author. 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 a crucial role in the theory of linear and nonlinear PDEs.
Chapter 1 (Introduction) describes the main motivations and intentions of this book. Chapter 2 is a selfcontained introduction into Morrey spaces.
Chapter 3 deals with hybrid smoothness spaces (which are between local and global 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 linear and nonlinear
heat equations in global and hybrid spaces. The obtained assertions about function spaces and nonlinear heat equations are used in the Chapters 5 and
6 to study Navier–Stokes equations in hybrid and global spaces.
This 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 Navier–Stokes equations as prototypes.07aDifferential equations2bicssc07aFunctional analysis2msc07aPartial differential equations2msc07aFourier analysis2msc07aIntegral equations2msc40uhttps://doi.org/10.4171/150423cover imageuhttps://www.ems-ph.org/img/books/triebel24_mini.jpg