Aspects Of Sobolev-type Inequalities (london Mathematical Society Lecture Note Series)
by Laurent Saloff-Coste /
2001 / English / PDF
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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.
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.
