000			06533nam a22003618i 4500
001			CR9780511549762
003			UkCbUP
005			20200124160239.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090511s2002||||enk o ||1 0|eng|d
020			_a9780511549762 (ebook)
020			_z9780521006071 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA323 _b.S35 2002
082	0	0	_a515/.782 _221
100	1		_aSaloff-Coste, L., _eauthor.
245	1	0	_aAspects of Sobolev-type inequalities / _cLaurent Saloff-Coste.
264		1	_aCambridge : _bCambridge University Press, _c2002.
300			_a1 online resource (x, 190 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLondon Mathematical Society lecture note series ; _v289
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_g1 _tSobolev inequalities in R[superscript n] _g7 -- _g1.1 _tSobolev inequalities _g7 -- _g1.1.2 _tThe proof due to Gagliardo and to Nirenberg _g9 -- _g1.1.3 _tp = 1 implies p [greater than or equal] 1 _g10 -- _g1.2 _tRiesz potentials _g11 -- _g1.2.1 _tAnother approach to Sobolev inequalities _g11 -- _g1.2.2 _tMarcinkiewicz interpolation theorem _g13 -- _g1.2.3 _tProof of Sobolev Theorem 1.2.1 _g16 -- _g1.3 _tBest constants _g16 -- _g1.3.1 _tThe case p = 1: isoperimetry _g16 -- _g1.3.2 _tA complete proof with best constant for p = 1 _g18 -- _g1.3.3 _tThe case p> 1 _g20 -- _g1.4 _tSome other Sobolev inequalities _g21 -- _g1.4.1 _tThe case p> n _g21 -- _g1.4.2 _tThe case p = n _g24 -- _g1.4.3 _tHigher derivatives _g26 -- _g1.5 _tSobolev -- Poincare inequalities on balls _g29 -- _g1.5.1 _tThe Neumann and Dirichlet eigenvalues _g29 -- _g1.5.2 _tPoincare inequalities on Euclidean balls _g30 -- _g1.5.3 _tSobolev -- Poincare inequalities _g31 -- _g2 _tMoser's elliptic Harnack inequality _g33 -- _g2.1 _tElliptic operators in divergence form _g33 -- _g2.1.1 _tDivergence form _g33 -- _g2.1.2 _tUniform ellipticity _g34 -- _g2.1.3 _tA Sobolev-type inequality for Moser's iteration _g37 -- _g2.2 _tSubsolutions and supersolutions _g38 -- _g2.2.1 _tSubsolutions _g38 -- _g2.2.2 _tSupersolutions _g43 -- _g2.2.3 _tAn abstract lemma _g47 -- _g2.3 _tHarnack inequalities and continuity _g49 -- _g2.3.1 _tHarnack inequalities _g49 -- _g2.3.2 _tHolder continuity _g50 -- _g3 _tSobolev inequalities on manifolds _g53 -- _g3.1.1 _tNotation concerning Riemannian manifolds _g53 -- _g3.1.2 _tIsoperimetry _g55 -- _g3.1.3 _tSobolev inequalities and volume growth _g57 -- _g3.2 _tWeak and strong Sobolev inequalities _g60 -- _g3.2.1 _tExamples of weak Sobolev inequalities _g60 -- _g3.2.2 _t(S[superscript [theta] subscript r, s])-inequalities: the parameters q and v _g61 -- _g3.2.3 _tThe case 0 <q <[infinity] _g63 -- _g3.2.4 _tThe case 1 = [infinity] _g66 -- _g3.2.5 _tThe case -[infinity] <q <0 _g68 -- _g3.2.6 _tIncreasing p _g70 -- _g3.2.7 _tLocal versions _g72 -- _g3.3.1 _tPseudo-Poincare inequalities _g73 -- _g3.3.2 _tPseudo-Poincare technique: local version _g75 -- _g3.3.3 _tLie groups _g77 -- _g3.3.4 _tPseudo-Poincare inequalities on Lie groups _g79 -- _g3.3.5 _tRicci [greater than or equal] 0 and maximal volume growth _g82 -- _g3.3.6 _tSobolev inequality in precompact regions _g85 -- _g4 _tTwo applications _g87 -- _g4.1 _tUltracontractivity _g87 -- _g4.1.1 _tNash inequality implies ultracontractivity _g87 -- _g4.1.2 _tThe converse _g91 -- _g4.2 _tGaussian heat kernel estimates _g93 -- _g4.2.1 _tThe Gaffney-Davies L[superscript 2] estimate _g93 -- _g4.2.2 _tComplex interpolation _g95 -- _g4.2.3 _tPointwise Gaussian upper bounds _g98 -- _g4.2.4 _tOn-diagonal lower bounds _g99 -- _g4.3 _tThe Rozenblum-Lieb-Cwikel inequality _g103 -- _g4.3.1 _tThe Schrodinger operator [Delta] -- V _g103 -- _g4.3.2 _tThe operator T[subscript V] = [Delta superscript -1]V _g105 -- _g4.3.3 _tThe Birman-Schwinger principle _g109 -- _g5 _tParabolic Harnack inequalities _g111 -- _g5.1 _tScale-invariant Harnack principle _g111 -- _g5.2 _tLocal Sobolev inequalities _g113 -- _g5.2.1 _tLocal Sobolev inequalities and volume growth _g113 -- _g5.2.2 _tMean value inequalities for subsolutions _g119 -- _g5.2.3 _tLocalized heat kernel upper bounds _g122 -- _g5.2.4 _tTime-derivative upper bounds _g127 -- _g5.2.5 _tMean value inequalities for supersolutions _g128 -- _g5.3 _tPoincare inequalities _g130 -- _g5.3.1 _tPoincare inequality and Sobolev inequality _g131 -- _g5.3.2 _tSome weighted Poincare inequalities _g133 -- _g5.3.3 _tWhitney-type coverings _g135 -- _g5.3.4 _tA maximal inequality and an application _g139 -- _g5.3.5 _tEnd of the proof of Theorem 5.3.4 _g141 -- _g5.4 _tHarnack inequalities and applications _g143 -- _g5.4.1 _tAn inequality for log u _g143 -- _g5.4.2 _tHarnack inequality for positive supersolutions _g145 -- _g5.4.3 _tHarnack inequalities for positive solutions _g146 -- _g5.4.4 _tHolder continuity _g149 -- _g5.4.5 _tLiouville theorems _g151 -- _g5.4.6 _tHeat kernel lower bounds _g152 -- _g5.4.7 _tTwo-sided heat kernel bounds _g154 -- _g5.5 _tThe parabolic Harnack principle _g155 -- _g5.5.1 _tPoincare, doubling, and Harnack _g157 -- _g5.5.2 _tStochastic completeness _g161 -- _g5.5.3 _tLocal Sobolev inequalities and the heat equation _g164 -- _g5.5.4 _tSelected applications of Theorem 5.5.1 _g168 -- _g5.6.1 _tUnimodular Lie groups _g172 -- _g5.6.2 _tHomogeneous spaces _g175 -- _g5.6.3 _tManifolds with Ricci curvature bounded below _g176.
520			_aThis 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	_aSobolev spaces.
650		0	_aInequalities (Mathematics)
776	0	8	_iPrint version: _z9780521006071
830		0	_aLondon Mathematical Society lecture note series ; _v289.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511549762
999			_c518326 _d518324