Aspects of Sobolev-type inequalities
Laurent Saloff-Coste
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.
Kategori:
Tahun:
2001
Edisi:
1
Penerbit:
Cambridge University Press
Bahasa:
english
Halaman:
202
ISBN 10:
0521006074
ISBN 13:
9780521006071
Nama seri:
London Mathematical Society Lecture Note Series
File:
DJVU, 2.86 MB
IPFS:
,
english, 2001
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