Stability of parabolic Harnack inequalities

By Martin T. Barlow, Richard F. Bass. 2003

123 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/95cf91d5e48ba0d5cbb4d76a6d5564d8dee03be9

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

In Geometry and Topology

Citations in the corpus

Discrete Curvature and Abelian Groups (2015, background): “_e graph point of view led to generalizations that would have been less natural in Riemannian geometry, such as β-parabolic Harnack inequalities (see, e.g., [5]) and to some counterexamples [4, 13,22].”
Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates (2018, background): “em3.7that fractional metric spaces for which dW >dH 1 must satisfy wBE() with = dW dH. Note that the hypothesis ofTheorem3.7is stable under rough isometries in the sense of Barlow-Bass-Kumagai [17,18,22] and is a part of the general theory of fractional diusions [10,12,13,15,16,19,20,38,50,51, a”
Quenched invariance principles for walks on clusters of percolation or among random conductances (2004, background): “With the help of known Gaussian bounds on the transition kernel of the walk, cf. Delmotte [10], Grigoryan-Telcs [12], Barlow-Bass [ 4 ], the main task is to show that for any M> 0,”
Characterization of sub‐Gaussian heat kernel estimates on strongly recurrent graphs (2005, methodology): “In [11], a characterization of C HK C β D;D was given in terms of a β -Poincaré inequality C PI C β D;D (see Section 1.”
Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps (2007, background): “BB ]. The case BB ] this is called the ‘cable system’ of G.) We write d for the metric on H. Extend g to a function h on H ◊H by linearity on each cable; then the conditions (5.9) and (5.10) imply that (5.11) also holds for h. So it is now enough to prove the Lemma for h.”
Volume growth and stochastic completeness of graphs (2012, methodology): “Varopoulos’ paper [31] establishes estimates for discrete time simple random walks using Brownian motion on metric graphs, and the paper of Barlow and Bass ([3]) uses Brownian motion on metric graphs to study a continuous time simple random walk.”
Harnack Inequalities: An Introduction (2007, background): “A parabolic Harnack inequality with a non-diffusive spacetime scaling is proved on infinite connected weighted graphs [117].”
Random walks on supercritical percolation clusters (2003, background): “See, for example, [BB3] for further details of this construction.”
Stability of parabolic Harnack inequalities on metric measure spaces (2006, background): “The following covering lemma holds; cf. [ BB5 ].”