On gradient estimates for heat kernels

2021 ◽  
Vol 46 (5) ◽  
pp. 717-779
Author(s):  
Baptiste Devyver
Keyword(s):  
Heat Kernels ◽  
Gradient Estimates

scholarly journals Uniform Gaussian Bounds for Subelliptic Heat Kernels and an Application to the Total Variation Flow of Graphs over Carnot Groups

2013 ◽  
Vol 1 ◽  
pp. 255-275 ◽  
Author(s):  
Luca Capogna ◽  
Giovanna Citti ◽  
Maria Manfredini
Keyword(s):  
Total Variation ◽  
Carnot Group ◽  
Riemannian Metrics ◽  
Heat Kernels ◽  
Gradient Estimates ◽  
Long Time Existence ◽  
Total Variation Flow ◽  
Long Time ◽  
Invariant Riemannian Metrics ◽  
Time Existence

Abstract In this paper we study heat kernels associated with a Carnot group G, endowed with a family of collapsing left-invariant Riemannian metrics σε which converge in the Gromov- Hausdorff sense to a sub-Riemannian structure on G as ε→ 0. The main new contribution are Gaussian-type bounds on the heat kernel for the σε metrics which are stable as ε→0 and extend the previous time-independent estimates in [16]. As an application we study well posedness of the total variation flow of graph surfaces over a bounded domain in a step two Carnot group (G; σε ). We establish interior and boundary gradient estimates, and develop a Schauder theory which are stable as ε → 0. As a consequence we obtain long time existence of smooth solutions of the sub-Riemannian flow (ε = 0), which in turn yield sub-Riemannian minimal surfaces as t → ∞.

scholarly journals Gradient estimates of Dirichlet heat kernels for unimodal Lévy processes

2017 ◽  
Vol 291 (2-3) ◽  
pp. 374-397 ◽  
Author(s):  
Tadeusz Kulczycki ◽  
Michał Ryznar
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Heat Kernels ◽  
Gradient Estimates

scholarly journals Gradient estimates for heat kernels and harmonic functions

2020 ◽  
Vol 278 (8) ◽  
pp. 108398 ◽  
Author(s):  
Thierry Coulhon ◽  
Renjin Jiang ◽  
Pekka Koskela ◽  
Adam Sikora
Keyword(s):  
Harmonic Functions ◽  
Heat Kernels ◽  
Gradient Estimates

scholarly journals Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces

2017 ◽  
Vol 272 (8) ◽  
pp. 3311-3346 ◽  
Author(s):  
Alexander Grigor'yan ◽  
Eryan Hu ◽  
Jiaxin Hu
Keyword(s):  
Dirichlet Forms ◽  
Heat Kernels ◽  
Metric Measure Spaces ◽  
Measure Spaces ◽  
Non Local
Sign in / Sign up

Export Citation Format

Share Document