Aspects of Sobolev-type inequalities / (Record no. 518326)
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| fixed length control field | 06533nam a22003618i 4500 |
| 001 - CONTROL NUMBER | |
| control field | CR9780511549762 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | UkCbUP |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200124160239.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
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| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr|||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 090511s2002||||enk o ||1 0|eng|d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780511549762 (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9780521006071 (paperback) |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UkCbUP |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | UkCbUP |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA323 |
| Item number | .S35 2002 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515/.782 |
| Edition number | 21 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Saloff-Coste, L., |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Aspects of Sobolev-type inequalities / |
| Statement of responsibility, etc | Laurent Saloff-Coste. |
| 264 #1 - Production, Publication, Distribution, Manufacture, and Copyright Notice (R) | |
| Place of production, publication, distribution, manufacture (R) | Cambridge : |
| Name of producer, publisher, distributor, manufacturer (R) | Cambridge University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2002. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (x, 190 pages) : |
| Other physical details | digital, PDF file(s). |
| 336 ## - Content Type (R) | |
| Content type term (R) | text |
| Content type code (R) | txt |
| Source (NR) | rdacontent |
| 337 ## - Media Type (R) | |
| Media type term (R) | computer |
| Media type code (R) | c |
| Source (NR) | rdamedia |
| 338 ## - Carrier Type (R) | |
| Carrier type term (R) | online resource |
| Carrier type code (R) | cr |
| Source (NR) | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| სერიის ცნობა | London Mathematical Society lecture note series ; |
| Volume number/sequential designation | 289 |
| 500 ## - GENERAL NOTE | |
| General note | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| 505 00 - FORMATTED CONTENTS NOTE | |
| Miscellaneous information | 1 |
| Title | Sobolev inequalities in R[superscript n] |
| Miscellaneous information | 7 -- |
| -- | 1.1 |
| Title | Sobolev inequalities |
| Miscellaneous information | 7 -- |
| -- | 1.1.2 |
| Title | The proof due to Gagliardo and to Nirenberg |
| Miscellaneous information | 9 -- |
| -- | 1.1.3 |
| Title | p = 1 implies p [greater than or equal] 1 |
| Miscellaneous information | 10 -- |
| -- | 1.2 |
| Title | Riesz potentials |
| Miscellaneous information | 11 -- |
| -- | 1.2.1 |
| Title | Another approach to Sobolev inequalities |
| Miscellaneous information | 11 -- |
| -- | 1.2.2 |
| Title | Marcinkiewicz interpolation theorem |
| Miscellaneous information | 13 -- |
| -- | 1.2.3 |
| Title | Proof of Sobolev Theorem 1.2.1 |
| Miscellaneous information | 16 -- |
| -- | 1.3 |
| Title | Best constants |
| Miscellaneous information | 16 -- |
| -- | 1.3.1 |
| Title | The case p = 1: isoperimetry |
| Miscellaneous information | 16 -- |
| -- | 1.3.2 |
| Title | A complete proof with best constant for p = 1 |
| Miscellaneous information | 18 -- |
| -- | 1.3.3 |
| Title | The case p> 1 |
| Miscellaneous information | 20 -- |
| -- | 1.4 |
| Title | Some other Sobolev inequalities |
| Miscellaneous information | 21 -- |
| -- | 1.4.1 |
| Title | The case p> n |
| Miscellaneous information | 21 -- |
| -- | 1.4.2 |
| Title | The case p = n |
| Miscellaneous information | 24 -- |
| -- | 1.4.3 |
| Title | Higher derivatives |
| Miscellaneous information | 26 -- |
| -- | 1.5 |
| Title | Sobolev -- Poincare inequalities on balls |
| Miscellaneous information | 29 -- |
| -- | 1.5.1 |
| Title | The Neumann and Dirichlet eigenvalues |
| Miscellaneous information | 29 -- |
| -- | 1.5.2 |
| Title | Poincare inequalities on Euclidean balls |
| Miscellaneous information | 30 -- |
| -- | 1.5.3 |
| Title | Sobolev -- Poincare inequalities |
| Miscellaneous information | 31 -- |
| -- | 2 |
| Title | Moser's elliptic Harnack inequality |
| Miscellaneous information | 33 -- |
| -- | 2.1 |
| Title | Elliptic operators in divergence form |
| Miscellaneous information | 33 -- |
| -- | 2.1.1 |
| Title | Divergence form |
| Miscellaneous information | 33 -- |
| -- | 2.1.2 |
| Title | Uniform ellipticity |
| Miscellaneous information | 34 -- |
| -- | 2.1.3 |
| Title | A Sobolev-type inequality for Moser's iteration |
| Miscellaneous information | 37 -- |
| -- | 2.2 |
| Title | Subsolutions and supersolutions |
| Miscellaneous information | 38 -- |
| -- | 2.2.1 |
| Title | Subsolutions |
| Miscellaneous information | 38 -- |
| -- | 2.2.2 |
| Title | Supersolutions |
| Miscellaneous information | 43 -- |
| -- | 2.2.3 |
| Title | An abstract lemma |
| Miscellaneous information | 47 -- |
| -- | 2.3 |
| Title | Harnack inequalities and continuity |
| Miscellaneous information | 49 -- |
| -- | 2.3.1 |
| Title | Harnack inequalities |
| Miscellaneous information | 49 -- |
| -- | 2.3.2 |
| Title | Holder continuity |
| Miscellaneous information | 50 -- |
| -- | 3 |
| Title | Sobolev inequalities on manifolds |
| Miscellaneous information | 53 -- |
| -- | 3.1.1 |
| Title | Notation concerning Riemannian manifolds |
| Miscellaneous information | 53 -- |
| -- | 3.1.2 |
| Title | Isoperimetry |
| Miscellaneous information | 55 -- |
| -- | 3.1.3 |
| Title | Sobolev inequalities and volume growth |
| Miscellaneous information | 57 -- |
| -- | 3.2 |
| Title | Weak and strong Sobolev inequalities |
| Miscellaneous information | 60 -- |
| -- | 3.2.1 |
| Title | Examples of weak Sobolev inequalities |
| Miscellaneous information | 60 -- |
| -- | 3.2.2 |
| Title | (S[superscript [theta] subscript r, s])-inequalities: the parameters q and v |
| Miscellaneous information | 61 -- |
| -- | 3.2.3 |
| Title | The case 0 <q <[infinity] |
| Miscellaneous information | 63 -- |
| -- | 3.2.4 |
| Title | The case 1 = [infinity] |
| Miscellaneous information | 66 -- |
| -- | 3.2.5 |
| Title | The case -[infinity] <q <0 |
| Miscellaneous information | 68 -- |
| -- | 3.2.6 |
| Title | Increasing p |
| Miscellaneous information | 70 -- |
| -- | 3.2.7 |
| Title | Local versions |
| Miscellaneous information | 72 -- |
| -- | 3.3.1 |
| Title | Pseudo-Poincare inequalities |
| Miscellaneous information | 73 -- |
| -- | 3.3.2 |
| Title | Pseudo-Poincare technique: local version |
| Miscellaneous information | 75 -- |
| -- | 3.3.3 |
| Title | Lie groups |
| Miscellaneous information | 77 -- |
| -- | 3.3.4 |
| Title | Pseudo-Poincare inequalities on Lie groups |
| Miscellaneous information | 79 -- |
| -- | 3.3.5 |
| Title | Ricci [greater than or equal] 0 and maximal volume growth |
| Miscellaneous information | 82 -- |
| -- | 3.3.6 |
| Title | Sobolev inequality in precompact regions |
| Miscellaneous information | 85 -- |
| -- | 4 |
| Title | Two applications |
| Miscellaneous information | 87 -- |
| -- | 4.1 |
| Title | Ultracontractivity |
| Miscellaneous information | 87 -- |
| -- | 4.1.1 |
| Title | Nash inequality implies ultracontractivity |
| Miscellaneous information | 87 -- |
| -- | 4.1.2 |
| Title | The converse |
| Miscellaneous information | 91 -- |
| -- | 4.2 |
| Title | Gaussian heat kernel estimates |
| Miscellaneous information | 93 -- |
| -- | 4.2.1 |
| Title | The Gaffney-Davies L[superscript 2] estimate |
| Miscellaneous information | 93 -- |
| -- | 4.2.2 |
| Title | Complex interpolation |
| Miscellaneous information | 95 -- |
| -- | 4.2.3 |
| Title | Pointwise Gaussian upper bounds |
| Miscellaneous information | 98 -- |
| -- | 4.2.4 |
| Title | On-diagonal lower bounds |
| Miscellaneous information | 99 -- |
| -- | 4.3 |
| Title | The Rozenblum-Lieb-Cwikel inequality |
| Miscellaneous information | 103 -- |
| -- | 4.3.1 |
| Title | The Schrodinger operator [Delta] -- V |
| Miscellaneous information | 103 -- |
| -- | 4.3.2 |
| Title | The operator T[subscript V] = [Delta superscript -1]V |
| Miscellaneous information | 105 -- |
| -- | 4.3.3 |
| Title | The Birman-Schwinger principle |
| Miscellaneous information | 109 -- |
| -- | 5 |
| Title | Parabolic Harnack inequalities |
| Miscellaneous information | 111 -- |
| -- | 5.1 |
| Title | Scale-invariant Harnack principle |
| Miscellaneous information | 111 -- |
| -- | 5.2 |
| Title | Local Sobolev inequalities |
| Miscellaneous information | 113 -- |
| -- | 5.2.1 |
| Title | Local Sobolev inequalities and volume growth |
| Miscellaneous information | 113 -- |
| -- | 5.2.2 |
| Title | Mean value inequalities for subsolutions |
| Miscellaneous information | 119 -- |
| -- | 5.2.3 |
| Title | Localized heat kernel upper bounds |
| Miscellaneous information | 122 -- |
| -- | 5.2.4 |
| Title | Time-derivative upper bounds |
| Miscellaneous information | 127 -- |
| -- | 5.2.5 |
| Title | Mean value inequalities for supersolutions |
| Miscellaneous information | 128 -- |
| -- | 5.3 |
| Title | Poincare inequalities |
| Miscellaneous information | 130 -- |
| -- | 5.3.1 |
| Title | Poincare inequality and Sobolev inequality |
| Miscellaneous information | 131 -- |
| -- | 5.3.2 |
| Title | Some weighted Poincare inequalities |
| Miscellaneous information | 133 -- |
| -- | 5.3.3 |
| Title | Whitney-type coverings |
| Miscellaneous information | 135 -- |
| -- | 5.3.4 |
| Title | A maximal inequality and an application |
| Miscellaneous information | 139 -- |
| -- | 5.3.5 |
| Title | End of the proof of Theorem 5.3.4 |
| Miscellaneous information | 141 -- |
| -- | 5.4 |
| Title | Harnack inequalities and applications |
| Miscellaneous information | 143 -- |
| -- | 5.4.1 |
| Title | An inequality for log u |
| Miscellaneous information | 143 -- |
| -- | 5.4.2 |
| Title | Harnack inequality for positive supersolutions |
| Miscellaneous information | 145 -- |
| -- | 5.4.3 |
| Title | Harnack inequalities for positive solutions |
| Miscellaneous information | 146 -- |
| -- | 5.4.4 |
| Title | Holder continuity |
| Miscellaneous information | 149 -- |
| -- | 5.4.5 |
| Title | Liouville theorems |
| Miscellaneous information | 151 -- |
| -- | 5.4.6 |
| Title | Heat kernel lower bounds |
| Miscellaneous information | 152 -- |
| -- | 5.4.7 |
| Title | Two-sided heat kernel bounds |
| Miscellaneous information | 154 -- |
| -- | 5.5 |
| Title | The parabolic Harnack principle |
| Miscellaneous information | 155 -- |
| -- | 5.5.1 |
| Title | Poincare, doubling, and Harnack |
| Miscellaneous information | 157 -- |
| -- | 5.5.2 |
| Title | Stochastic completeness |
| Miscellaneous information | 161 -- |
| -- | 5.5.3 |
| Title | Local Sobolev inequalities and the heat equation |
| Miscellaneous information | 164 -- |
| -- | 5.5.4 |
| Title | Selected applications of Theorem 5.5.1 |
| Miscellaneous information | 168 -- |
| -- | 5.6.1 |
| Title | Unimodular Lie groups |
| Miscellaneous information | 172 -- |
| -- | 5.6.2 |
| Title | Homogeneous spaces |
| Miscellaneous information | 175 -- |
| -- | 5.6.3 |
| Title | Manifolds with Ricci curvature bounded below |
| Miscellaneous information | 176. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | This book, first published in 2001, focuses on Poincaré, Nash and other Sobolev-type inequalities and their applications to the Laplace and heat diffusion equations on Riemannian manifolds. Applications covered include the ultracontractivity of the heat diffusion semigroup, Gaussian heat kernel bounds, the Rozenblum-Lieb-Cwikel inequality and elliptic and parabolic Harnack inequalities. Emphasis is placed on the role of families of local Poincaré and Sobolev inequalities. The text provides the first self contained account of the equivalence between the uniform parabolic Harnack inequality, on the one hand, and the conjunction of the doubling volume property and Poincaré's inequality on the other. It is suitable to be used as an advanced graduate textbook and will also be a useful source of information for graduate students and researchers in analysis on manifolds, geometric differential equations, Brownian motion and diffusion on manifolds, as well as other related areas. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Sobolev spaces. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Inequalities (Mathematics) |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Print version: |
| International Standard Book Number | 9780521006071 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | London Mathematical Society lecture note series ; |
| Volume number/sequential designation | 289. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1017/CBO9780511549762">https://doi.org/10.1017/CBO9780511549762</a> |
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