3 citations · 3 across the 6 of their papers we have counts for
4 papers · 1 filter
A tree-like fractal Dirichlet space lying between strong and weak elliptic Harnack inequalities
Caoxu Huang, Guanhua Liu
In this paper we construct a self-similar fractal configured as an infinitely branched tree and equip it with a regular self-similar Dirichlet form. We show anomalous behaviour of…
Inhomogeneous Scaling Function and Heat Kernel Estimates on Fractals Satisfying Some Resistance Conditions
Diwen Chang, Guanhua Liu
In this paper, we focus on strongly local regular Dirichlet forms, especially those satisfying Morrey-type inequalities. We prove the equivalence between resistance estimates and h…
The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis
Guanhua Liu
This paper provides the general theory on parabolic Harnack inequalities (PHI, for short) for regular Dirichlet forms without killing part. We prove PHI by pure analytic methods, u…
Weak parabolic Harnack inequality and Hölder regularity for non-local Dirichlet forms
Guanhua Liu
In this paper we give equivalent conditions for the weak parabolic Harnack inequality for general regular Dirichlet forms without killing part, in terms of local heat kernel estima…