02382nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002900185100002800214245010100242260008200343300003400425336002600459337002600485338003600511347002400547490004000571506006600611520111500677650003201792650002901824650004001853650002601893856003201919856006901951166-130529CH-001817-320130529234500.0a fot ||| 0|cr nn mmmmamaa130529e20130529sz fot ||| 0|eng d a978303719623670a10.4171/1232doi ach0018173 7aPBKG2bicssc a46-xxa35-xxa42-xx2msc1 aTriebel, Hans,eauthor.10aLocal Function Spaces, Heat and Navier–Stokes Equationsh[electronic resource] /cHans Triebel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2013 a1 online resource (241 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v201 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aIn 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 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.07aFunctional analysis2bicssc07aFunctional analysis2msc07aPartial differential equations2msc07aFourier analysis2msc40uhttps://doi.org/10.4171/123423cover imageuhttps://www.ems-ph.org/img/books/triebel20_mini.jpg