Aspects of Sobolev-type inequalities

By L. Saloff‐Coste. 2001

611 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/394e99be87c93d7aa53ecb2e3294bdf9ecd3baf0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

Citations in the corpus

Stability of parabolic Harnack inequalities on metric measure spaces (2006, background): “When β̄ = β = 2, the study of the parabolic Harnack inequality has a long history (see [Da], [SC2] etc.”
Weighted Poincaré inequality and heat kernel estimates for finite range jump processes (2008, background): “(For the details on (weighted) Poincaré inequality and lower bound estimate of heat kernels for diffusions, we refer our readers to [14,22,29,30] and the references therein.”
On the equivalence of parabolic Harnack inequalities and heat kernel estimates (2012, background): “We do not touch here on the interesting question of deducing either the Harnack inequality or the heat kernel bounds from some simpler properties, and refer the reader to [6], [14], [33], [34] and references therein.”
Harnack inequalities on weighted graphs and some applications to the random conductance model (2013, neutral): “We refer to the monograph [32] for more details on this topic.”
Heat Kernel Generated Frames in the Setting of Dirichlet Spaces (2012, background): “7) (see [27, 28, 53, 57], and the references therein).”
Approximate McKean–Vlasov representations for a class of SPDEs (2005, background): “For φ ∈ C 1 (R) the following identity holds true (see, for example, [25] page 12)”
A priori Holder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps (2008, background): “(See, for example, [ SC , Theorem 5.3.4] for the proof.)”
Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds (2005, methodology): “In a very similar way, this method has been used ea by Varopoulos [69] and Saloff-Coste [59] in the study ofL∞-bound of time derivatives o the heat kernel of the Laplace–Beltrami operator on complete Riemannian manifold Proposition 5.8.”