LEADER 03479nam 22006015 450 001 996466504603316 005 20200702161707.0 010 $a3-540-45168-4 024 7 $a10.1007/BFb0103908 035 $a(CKB)1000000000437278 035 $a(SSID)ssj0000325239 035 $a(PQKBManifestationID)11239186 035 $a(PQKBTitleCode)TC0000325239 035 $a(PQKBWorkID)10340062 035 $a(PQKB)11458990 035 $a(DE-He213)978-3-540-45168-6 035 $a(MiAaPQ)EBC5591445 035 $a(PPN)155176722 035 $a(EXLCZ)991000000000437278 100 $a20121227d2000 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aNonlinear Potential Theory and Weighted Sobolev Spaces$b[electronic resource] /$fby Bengt O. Turesson 205 $a1st ed. 2000. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2000. 215 $a1 online resource (XII, 180 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1736 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-67588-4 320 $aIncludes bibliographical references (pages [163]-170) and index. 327 $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(Ű) -- 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. 330 $aThe book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1736 606 $aPotential theory (Mathematics) 606 $aPartial differential equations 606 $aPotential Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12163 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aPotential theory (Mathematics). 615 0$aPartial differential equations. 615 14$aPotential Theory. 615 24$aPartial Differential Equations. 676 $a515.23 700 $aTuresson$b Bengt O$4aut$4http://id.loc.gov/vocabulary/relators/aut$01064296 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466504603316 996 $aNonlinear Potential Theory and Weighted Sobolev Spaces$92537339 997 $aUNISA