Aspects of Sobolev-type inequalities /
Saloff-Coste, L.,
Aspects of Sobolev-type inequalities / Laurent Saloff-Coste. - Cambridge : Cambridge University Press, 2002. - 1 online resource (x, 190 pages) : digital, PDF file(s). - London Mathematical Society lecture note series ; 289 . - London Mathematical Society lecture note series ; 289. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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
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.
9780511549762 (ebook)
Sobolev spaces.
Inequalities (Mathematics)
QA323 / .S35 2002
515/.782
Aspects of Sobolev-type inequalities / Laurent Saloff-Coste. - Cambridge : Cambridge University Press, 2002. - 1 online resource (x, 190 pages) : digital, PDF file(s). - London Mathematical Society lecture note series ; 289 . - London Mathematical Society lecture note series ; 289. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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
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.
9780511549762 (ebook)
Sobolev spaces.
Inequalities (Mathematics)
QA323 / .S35 2002
515/.782