ﻻ يوجد ملخص باللغة العربية
It is known that the couple formed by the two dimensional Brownian motion and its Levy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The associated diffusion operator is hypoelliptic but not elliptic, which makes difficult the derivation of functional inequalities for the heat kernel. However, Driver and Melcher and more recently H.-Q. Li have obtained useful gradient bounds for the heat kernel on the Heisenberg group. We provide in this paper simple proofs of these bounds, and explore their consequences in terms of functional inequalities, including Cheeger and Bobkov type isoperimetric inequalities for the heat kernel.
This paper presents a detailed analysis of the heat kernel on an $(mathbb{N}timesmathbb{N})$-parameter family of compact metric measure spaces, which do not satisfy the volume doubling property. In particular, uniform bounds of the heat kernel and it
We give a direct proof of the sharp two-sided estimates, recently established in [4,9], for the Dirichlet heat kernel of the fractional Laplacian with gradient perturbation in $C^{1, 1}$ open sets by using Duhamel formula. We also obtain a gradient e
We investigate observability and Lipschitz stability for the Heisenberg heat equation on the rectangular domain $$Omega = (-1,1)timesmathbb{T}timesmathbb{T}$$ taking as observation regions slices of the form $omega=(a,b) times mathbb{T} times mathbb{
In this paper, we obtain upper and lower bounds for the moments of the solution to a class of fractional stochastic heat equations on the ball driven by a Gaussian noise which is white in time, and with a spatial correlation in space of Riesz kernel
By using Duhamels formula, we prove sharp two-sided estimates for the heat kernel of spectral fractional Laplacian with time-dependent gradient perturbation in bounded $C^{1,1}$ domains. Moreover, we also obtain gradient estimate as well as Holder continuity of the gradient of the heat kernel.