000 03127nam a22004815i 4500
001 978-3-540-45168-6
003 DE-He213
005 20190213151833.0
007 cr nn 008mamaa
008 121227s2000 gw | s |||| 0|eng d
020 _a9783540451686
_9978-3-540-45168-6
024 7 _a10.1007/BFb0103908
_2doi
050 4 _aQA404.7-405
072 7 _aPBWL
_2bicssc
072 7 _aMAT033000
_2bisacsh
072 7 _aPBWL
_2thema
082 0 4 _a515.96
_223
100 1 _aTuresson, Bengt Ove.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aNonlinear Potential Theory and Weighted Sobolev Spaces
_h[electronic resource] /
_cby Bengt Ove Turesson.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2000.
300 _aXII, 180 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1736
505 0 _aIntroduction -- Preliminaries: Notation and conventions. Basic results concerning weights -- Sobolev spaces: The Sobolev space $W^(mp) w (/Omega)$. The Sobolev space $W^(mp) w (/Omega)$. Hausdorff measures. Isoperimetric inequalities. Some Sobolev type inequalities. Embeddings into L^q µ(Û) -- Potential theory: Norm inequalities for fractional integrals and maximal functions. Meyers' Theory for Lp-capacities. Bessel and Riesz capacities. Hausdorff capacities. Variational capacities. Thinness: The case 1< p.
520 _aThe book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.
650 0 _aPotential theory (Mathematics).
650 0 _aDifferential equations, partial.
650 1 4 _aPotential Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M12163
650 2 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540675884
776 0 8 _iPrinted edition:
_z9783662165737
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1736
856 4 0 _uhttps://doi.org/10.1007/BFb0103908
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c12048
_d12048