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Aspects of Sobolev-type inequalities /
Focusing on Poincaré, Nash and other Sobolev-type inequalities and their applications to the Laplace and heat diffusion equations on Riemannian manifolds, this text is an advanced graduate book that will also suit researchers.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
2002.
|
| Colección: | London Mathematical Society lecture note series ;
289. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Saloff-Coste, L. | |
| 245 | 1 | 0 | |a Aspects of Sobolev-type inequalities / |c Laurent Saloff-Coste. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 2002. | ||
| 300 | |a 1 online resource (x, 190 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 289 | |
| 504 | |a Includes bibliographical references (pages 183-188) and index. | ||
| 505 | 0 | 0 | |g 1 |t Sobolev inequalities in R[superscript n] |g 7 -- |g 1.1 |t Sobolev inequalities |g 7 -- |g 1.1.2 |t The proof due to Gagliardo and to Nirenberg |g 9 -- |g 1.1.3 |t p = 1 implies p [greater than or equal] 1 |g 10 -- |g 1.2 |t Riesz potentials |g 11 -- |g 1.2.1 |t Another approach to Sobolev inequalities |g 11 -- |g 1.2.2 |t Marcinkiewicz interpolation theorem |g 13 -- |g 1.2.3 |t Proof of Sobolev Theorem 1.2.1 |g 16 -- |g 1.3 |t Best constants |g 16 -- |g 1.3.1 |t The case p = 1: isoperimetry |g 16 -- |g 1.3.2 |t A complete proof with best constant for p = 1 |g 18 -- |g 1.3.3 |t The case p> 1 |g 20 -- |g 1.4 |t Some other Sobolev inequalities |g 21 -- |g 1.4.1 |t The case p> n |g 21 -- |g 1.4.2 |t The case p = n |g 24 -- |g 1.4.3 |t Higher derivatives |g 26 -- |g 1.5 |t Sobolev -- Poincare inequalities on balls |g 29 -- |g 1.5.1 |t The Neumann and Dirichlet eigenvalues |g 29 -- |g 1.5.2 |t Poincare inequalities on Euclidean balls |g 30 -- |g 1.5.3 |t Sobolev -- Poincare inequalities |g 31 -- |g 2 |t Moser's elliptic Harnack inequality |g 33 -- |g 2.1 |t Elliptic operators in divergence form |g 33 -- |g 2.1.1 |t Divergence form |g 33 -- |g 2.1.2 |t Uniform ellipticity |g 34 -- |g 2.1.3 |t A Sobolev-type inequality for Moser's iteration |g 37 -- |g 2.2 |t Subsolutions and supersolutions |g 38 -- |g 2.2.1 |t Subsolutions |g 38 -- |g 2.2.2 |t Supersolutions |g 43 -- |g 2.2.3 |t An abstract lemma |g 47 -- |g 2.3 |t Harnack inequalities and continuity |g 49 -- |g 2.3.1 |t Harnack inequalities |g 49 -- |g 2.3.2 |t Holder continuity |g 50 -- |g 3 |t Sobolev inequalities on manifolds |g 53 -- |g 3.1.1 |t Notation concerning Riemannian manifolds |g 53 -- |g 3.1.2 |t Isoperimetry |g 55 -- |g 3.1.3 |t Sobolev inequalities and volume growth |g 57 -- |g 3.2 |t Weak and strong Sobolev inequalities |g 60 -- |g 3.2.1 |t Examples of weak Sobolev inequalities |g 60 -- |g 3.2.2 |t (S[superscript [theta] subscript r, s])-inequalities: the parameters q and v |g 61 -- |g 3.2.3 |t The case 0 <q <[infinity] |g 63 -- |g 3.2.4 |t The case 1 = [infinity] |g 66 -- |g 3.2.5 |t The case -[infinity] <q <0 |g 68 -- |g 3.2.6 |t Increasing p |g 70 -- |g 3.2.7 |t Local versions |g 72 -- |g 3.3.1 |t Pseudo-Poincare inequalities |g 73 -- |g 3.3.2 |t Pseudo-Poincare technique: local version |g 75 -- |g 3.3.3 |t Lie groups |g 77 -- |g 3.3.4 |t Pseudo-Poincare inequalities on Lie groups |g 79 -- |g 3.3.5 |t Ricci [greater than or equal] 0 and maximal volume growth |g 82 -- |g 3.3.6 |t Sobolev inequality in precompact regions |g 85 -- |g 4 |t Two applications |g 87 -- |g 4.1 |t Ultracontractivity |g 87 -- |g 4.1.1 |t Nash inequality implies ultracontractivity |g 87 -- |g 4.1.2 |t The converse |g 91 -- |g 4.2 |t Gaussian heat kernel estimates |g 93 -- |g 4.2.1 |t The Gaffney-Davies L[superscript 2] estimate |g 93 -- |g 4.2.2 |t Complex interpolation |g 95 -- |g 4.2.3 |t Pointwise Gaussian upper bounds |g 98 -- |g 4.2.4 |t On-diagonal lower bounds |g 99 -- |g 4.3 |t The Rozenblum-Lieb-Cwikel inequality |g 103 -- |g 4.3.1 |t The Schrodinger operator [Delta] -- V |g 103 -- |g 4.3.2 |t The operator T[subscript V] = [Delta superscript -1]V |g 105 -- |g 4.3.3 |t The Birman-Schwinger principle |g 109 -- |g 5 |t Parabolic Harnack inequalities |g 111 -- |g 5.1 |t Scale-invariant Harnack principle |g 111 -- |g 5.2 |t Local Sobolev inequalities |g 113 -- |g 5.2.1 |t Local Sobolev inequalities and volume growth |g 113 -- |g 5.2.2 |t Mean value inequalities for subsolutions |g 119 -- |g 5.2.3 |t Localized heat kernel upper bounds |g 122 -- |g 5.2.4 |t Time-derivative upper bounds |g 127 -- |g 5.2.5 |t Mean value inequalities for supersolutions |g 128 -- |g 5.3 |t Poincare inequalities |g 130 -- |g 5.3.1 |t Poincare inequality and Sobolev inequality |g 131 -- |g 5.3.2 |t Some weighted Poincare inequalities |g 133 -- |g 5.3.3 |t Whitney-type coverings |g 135 -- |g 5.3.4 |t A maximal inequality and an application |g 139 -- |g 5.3.5 |t End of the proof of Theorem 5.3.4 |g 141 -- |g 5.4 |t Harnack inequalities and applications |g 143 -- |g 5.4.1 |t An inequality for log u |g 143 -- |g 5.4.2 |t Harnack inequality for positive supersolutions |g 145 -- |g 5.4.3 |t Harnack inequalities for positive solutions |g 146 -- |g 5.4.4 |t Holder continuity |g 149 -- |g 5.4.5 |t Liouville theorems |g 151 -- |g 5.4.6 |t Heat kernel lower bounds |g 152 -- |g 5.4.7 |t Two-sided heat kernel bounds |g 154 -- |g 5.5 |t The parabolic Harnack principle |g 155 -- |g 5.5.1 |t Poincare, doubling, and Harnack |g 157 -- |g 5.5.2 |t Stochastic completeness |g 161 -- |g 5.5.3 |t Local Sobolev inequalities and the heat equation |g 164 -- |g 5.5.4 |t Selected applications of Theorem 5.5.1 |g 168 -- |g 5.6.1 |t Unimodular Lie groups |g 172 -- |g 5.6.2 |t Homogeneous spaces |g 175 -- |g 5.6.3 |t Manifolds with Ricci curvature bounded below |g 176. |
| 520 | |a Focusing on Poincaré, Nash and other Sobolev-type inequalities and their applications to the Laplace and heat diffusion equations on Riemannian manifolds, this text is an advanced graduate book that will also suit researchers. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Sobolev spaces. | |
| 650 | 0 | |a Inequalities (Mathematics) | |
| 650 | 6 | |a Espaces de Sobolev. | |
| 650 | 6 | |a Inégalités (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Functional Analysis. |2 bisacsh | |
| 650 | 7 | |a Inequalities (Mathematics) |2 fast | |
| 650 | 7 | |a Sobolev spaces |2 fast | |
| 650 | 7 | |a Sobolevsche Ungleichung |2 gnd | |
| 650 | 1 | 7 | |a Sobolev ruimten. |2 gtt |
| 650 | 1 | 7 | |a Vergelijkingen (wiskunde) |2 gtt |
| 650 | 7 | |a Desigualdades (análise matemática) |2 larpcal | |
| 776 | 0 | 8 | |i Print version: |a Saloff-Coste, L. |t Aspects of Sobolev-type inequalities. |d Cambridge ; New York : Cambridge University Press, 2002 |z 0521006074 |w (DLC) 2001035237 |w (OCoLC)46810848 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 289. | |
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