TY  - BOOK
AU  - Saloff-Coste,L.
TI  - Aspects of Sobolev-type inequalitiesLaurent Saloff-Coste
T2  - London Mathematical Society lecture note series
SN  - 9781107360747
AV  - QA323 .A874 2002
PY  - 2002///
CY  - Cambridge, New York
PB  - Cambridge University Press
KW  - Sobolev spaces
KW  - Inequalities (Mathematics)
KW  - Electronic Books
N1  - 2; Sobolev inequalities in R[superscript n] --; Sobolev inequalities --; The proof due to Gagliardo and to Nirenberg --; p = 1 implies p [greater than or equal] 1 --; Riesz potentials --; Another approach to Sobolev inequalities --; Marcinkiewicz interpolation theorem --; Proof of Sobolev Theorem 1.2.1 --; Best constants --; The case p = 1: isoperimetry --; A complete proof with best constant for p = 1 --; The case p > 1 --; Some other Sobolev inequalities --; The case p > n --; The case p = n --; Higher derivatives --; Sobolev --; Poincare inequalities on balls --; The Neumann and Dirichlet eigenvalues --; Poincare inequalities on Euclidean balls --; Sobolev --; Poincare inequalities --; Moser's elliptic Harnack inequality --; Elliptic operators in divergence form --; Divergence form --; Uniform ellipticity --; A Sobolev-type inequality for Moser's iteration --; Subsolutions and supersolutions --; Subsolutions --; Supersolutions --; An abstract lemma --; Harnack inequalities and continuity --; Harnack inequalities --; Holder continuity --; Sobolev inequalities on manifolds --; Notation concerning Riemannian manifolds --; Isoperimetry --; Sobolev inequalities and volume growth --; Weak and strong Sobolev inequalities --; Examples of weak Sobolev inequalities --; (S[superscript [theta] subscript r,s])-inequalities: the parameters q and v --; The case 0 < q < [infinity] --; The case 1 = [infinity] --; The case -[infinity] < q < 0 --; Increasing p --; Local versions --; Pseudo-Poincare inequalities --; Pseudo-Poincare technique: local version --; Lie groups --; Pseudo-Poincare inequalities on Lie groups --; Ricci [greater than or equal] 0 and maximal volume growth --; Sobolev inequality in precompact regions --; Two applications --; Ultracontractivity --; Nash inequality implies ultracontractivity --; The converse --; Gaussian heat kernel estimates --; The Gaffney-Davies L[superscript 2. estimate --; Complex interpolation --; Pointwise Gaussian upper bounds --; On-diagonal lower bounds --; The Rozenblum-Lieb-Cwikel inequality --; The Schrodinger operator [Delta] --; V --; The operator T[subscript V] = [Delta superscript -1.V --; The Birman-Schwinger principle --; Parabolic Harnack inequalities --; Scale-invariant Harnack principle --; Local Sobolev inequalities --; Local Sobolev inequalities and volume growth --; Mean value inequalities for subsolutions --; Localized heat kernel upper bounds --; Time-derivative upper bounds --; Mean value inequalities for supersolutions --; Poincare inequalities --; Poincare inequality and Sobolev inequality --; Some weighted Poincare inequalities --; Whitney-type coverings --; A maximal inequality and an application --; End of the proof of Theorem 5.3.4 --; Harnack inequalities and applications --; An inequality for log u --; Harnack inequality for positive supersolutions --; Harnack inequalities for positive solutions --; Holder continuity --; Liouville theorems --; Heat kernel lower bounds --; Two-sided heat kernel bounds --; The parabolic Harnack principle --; Poincare, doubling, and Harnack --; Stochastic completeness --; Local Sobolev inequalities and the heat equation --; Selected applications of Theorem 5.5.1 --; Unimodular Lie groups --; Homogeneous spaces --; Manifolds with Ricci curvature bounded below; 2; b
N2  - 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
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