Buch, Englisch, Band 289, 202 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 336 g
Buch, Englisch, Band 289, 202 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 336 g
Reihe: London Mathematical Society Lecture Note Series
ISBN: 978-0-521-00607-1
Verlag: Cambridge University Press
This book 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.
Autoren/Hrsg.
Weitere Infos & Material
Preface; Introduction; 1. Sobolev inequalities in Rn; 2. Moser's elliptic Harnack Inequality; 3. Sobolev inequalities on manifolds; 4. Two applications; 5. Parabolic Harnack inequalities.
