000 | 02949nam a22004815i 4500 | ||
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001 | 978-3-540-45168-6 | ||
003 | DE-He213 | ||
005 | 20160624101820.0 | ||
007 | cr nn 008mamaa | ||
008 | 121227s2000 gw | s |||| 0|eng d | ||
020 |
_a9783540451686 _9978-3-540-45168-6 |
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024 | 7 |
_a10.1007/BFb0103908 _2doi |
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050 | 4 | _aQA404.7-405 | |
072 | 7 |
_aPBWL _2bicssc |
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072 | 7 |
_aMAT033000 _2bisacsh |
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082 | 0 | 4 |
_a515.96 _223 |
100 | 1 |
_aTuresson, Bengt Ove. _eauthor. |
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245 | 1 | 0 |
_aNonlinear Potential Theory and Weighted Sobolev Spaces _h[electronic resource] / _cby Bengt Ove Turesson. |
260 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2000. |
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264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2000. |
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300 |
_aXII, 180 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1736 |
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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 | _aMathematics. | |
650 | 0 | _aDifferential equations, partial. | |
650 | 0 | _aPotential theory (Mathematics). | |
650 | 1 | 4 | _aMathematics. |
650 | 2 | 4 | _aPotential Theory. |
650 | 2 | 4 | _aPartial Differential Equations. |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783540675884 |
786 | _dSpringer | ||
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1736 |
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856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/BFb0103908 |
942 |
_2EBK1304 _cEBK |
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999 |
_c30598 _d30598 |