LEADER 01016nam0 22002531i 450 001 UON00042773 005 20231205102153.376 100 $a20020107d1980 |0itac50 ba 101 $arus 102 $aSU 105 $a|||| 1|||| 200 1 $aIzvestija$eXussar irystony zonad-irtasaeg Instituty Uactae 210 $aTblisi$cIzd. Mecniereba$d1980 215 $a v.$d26 c 300 $aposs. vol. XXV ; In testa al front. : Akademija Nauk Gruzinskoj SSR, Jugo-oestinskij Naucno-issledovatel'skij Institut 620 $aGE$dTbilisi$3UONL000567 686 $aCAU I$cCAUCASO E ARMENIA - GENERALIA$2A 712 $aIzdatel'stvo Akademii Nauk Gruzinskoj SSR$3UONV247378$4650 801 $aIT$bSOL$c20240220$gRICA 899 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$2UONSI 912 $aUON00042773 950 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI CAU I 012 $eSI SA 37324 5 012 996 $aIzvestija$91152914 997 $aUNIOR LEADER 03269nam 22006015 450 001 9910146315903321 005 20250729101819.0 010 $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 /$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 $aLecture Notes in Mathematics,$x1617-9692 ;$v1736 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$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,$x1617-9692 ;$v1736 606 $aPotential theory (Mathematics) 606 $aDifferential equations 606 $aPotential Theory 606 $aDifferential Equations 615 0$aPotential theory (Mathematics) 615 0$aDifferential equations. 615 14$aPotential Theory. 615 24$aDifferential 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 $a9910146315903321 996 $aNonlinear Potential Theory and Weighted Sobolev Spaces$92537339 997 $aUNINA