000			04928nam a2200373Ki 4500
001			ocn839304256
003			OCoLC
005			20240726105348.0
008			130415s2002 enka ob 001 0 eng d
040			_aNT _beng _erda _cNT
020			_a9781107360747 _q((electronic)l(electronic)ctronic)l((electronic)l(electronic)ctronic)ctronic bk.
050	0	4	_aQA323 _b.A874 2002
049			_aNTA
100	1		_aSaloff-Coste, L. _e1
245	1	0	_aAspects of Sobolev-type inequalitiesLaurent Saloff-Coste.
260			_aCambridge ; _aNew York : _bCambridge University Press, _c(c)2002.
300			_a1 online resource (x, 190 pages) : _billustrations.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_adata file _2rda
490	1		_aLondon Mathematical Society lecture note series ; _v289
504			_a2
505	0	0	_tSobolev inequalities in R[superscript n] -- _tSobolev inequalities -- _tThe proof due to Gagliardo and to Nirenberg -- _tp = 1 implies p [greater than or equal] 1 -- _tRiesz potentials -- _tAnother approach to Sobolev inequalities -- _tMarcinkiewicz interpolation theorem -- _tProof of Sobolev Theorem 1.2.1 -- _tBest constants -- _tThe case p = 1: isoperimetry -- _tA complete proof with best constant for p = 1 -- _tThe case p > 1 -- _tSome other Sobolev inequalities -- _tThe case p > n -- _tThe case p = n -- _tHigher derivatives -- _tSobolev -- _tPoincare inequalities on balls -- _tThe Neumann and Dirichlet eigenvalues -- _tPoincare inequalities on Euclidean balls -- _tSobolev -- _tPoincare inequalities -- _tMoser's elliptic Harnack inequality -- _tElliptic operators in divergence form -- _tDivergence form -- _tUniform ellipticity -- _tA Sobolev-type inequality for Moser's iteration -- _tSubsolutions and supersolutions -- _tSubsolutions -- _tSupersolutions -- _tAn abstract lemma -- _tHarnack inequalities and continuity -- _tHarnack inequalities -- _tHolder continuity -- _tSobolev inequalities on manifolds -- _tNotation concerning Riemannian manifolds -- _tIsoperimetry -- _tSobolev inequalities and volume growth -- _tWeak and strong Sobolev inequalities -- _tExamples of weak Sobolev inequalities -- _t(S[superscript [theta] subscript r,s])-inequalities: the parameters q and v -- _tThe case 0 < q < [infinity] -- _tThe case 1 = [infinity] -- _tThe case -[infinity] < q < 0 -- _tIncreasing p -- _tLocal versions -- _tPseudo-Poincare inequalities -- _tPseudo-Poincare technique: local version -- _tLie groups -- _tPseudo-Poincare inequalities on Lie groups -- _tRicci [greater than or equal] 0 and maximal volume growth -- _tSobolev inequality in precompact regions -- _tTwo applications -- _tUltracontractivity -- _tNash inequality implies ultracontractivity -- _tThe converse -- _tGaussian heat kernel estimates -- _tThe Gaffney-Davies L[superscript 2. estimate -- _tComplex interpolation -- _tPointwise Gaussian upper bounds -- _tOn-diagonal lower bounds -- _tThe Rozenblum-Lieb-Cwikel inequality -- _tThe Schrodinger operator [Delta] -- _tV -- _tThe operator T[subscript V] = [Delta superscript -1.V -- _tThe Birman-Schwinger principle -- _tParabolic Harnack inequalities -- _tScale-invariant Harnack principle -- _tLocal Sobolev inequalities -- _tLocal Sobolev inequalities and volume growth -- _tMean value inequalities for subsolutions -- _tLocalized heat kernel upper bounds -- _tTime-derivative upper bounds -- _tMean value inequalities for supersolutions -- _tPoincare inequalities -- _tPoincare inequality and Sobolev inequality -- _tSome weighted Poincare inequalities -- _tWhitney-type coverings -- _tA maximal inequality and an application -- _tEnd of the proof of Theorem 5.3.4 -- _tHarnack inequalities and applications -- _tAn inequality for log u -- _tHarnack inequality for positive supersolutions -- _tHarnack inequalities for positive solutions -- _tHolder continuity -- _tLiouville theorems -- _tHeat kernel lower bounds -- _tTwo-sided heat kernel bounds -- _tThe parabolic Harnack principle -- _tPoincare, doubling, and Harnack -- _tStochastic completeness -- _tLocal Sobolev inequalities and the heat equation -- _tSelected applications of Theorem 5.5.1 -- _tUnimodular Lie groups -- _tHomogeneous spaces -- _tManifolds with Ricci curvature bounded below
520	0		_aFocusing 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.
530			_a2 _ub
650		0	_aSobolev spaces.
650		0	_aInequalities (Mathematics)
655		1	_aElectronic Books.
856	4	0	_uhttps://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=552338&site=eds-live&custid=s3260518 _zClick to access digital title | log in using your CIU ID number and my.ciu.edu password
942			_cOB _D _eEB _hQA _m2002 _QOL _R _x _8NFIC _2LOC
994			_a02 _bNT
999			_c97883 _d97883
902			_a1 _bCynthia Snell _c1 _dCynthia Snell