Related papers: Heat kernel bounds for parabolic equations with si…

We obtain lower and upper bounds on the heat kernel and Green functions of the Schroedinger operator in a random Gaussian magnetic field and a fixed scalar potential. We apply stochastic Feynman-Kac representation, diamagnetic upper bounds…

We study the random conductance model on $\mathbb{Z}^d$ with ergodic, unbounded conductances. We prove a Gaussian lower bound on the heat kernel given a polynomial moment condition and some additional assumptions on the correlations of the…

Using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernels of some nonautonomous Kolmogorov operators with possibly unbounded drift and diffusion coefficients and a possibly unbounded potential term.

This is first of series papers on new two-side Gaussian bounds for the heat kernel $H(x,y,t)$ on a complete manifold $(M,g)$. In this paper, on a complete manifold $M$ with $Ric(M)\geq 0$, we obtain new two-side Gaussian bounds for the heat…

We prove pointwise and $L^p$ gradient estimates for the heat kernel on the bounded and unbounded Vicsek set and applications to Sobolev inequalities are given. We also define a Hodge semigroup in that setting and prove estimates for its…

We establish sharp upper and lower bounds of Gaussian type for the heat kernel in the metric measure space satisfying $\RCD(0,N)$ ( equivalently, $\RCD^\ast(0,N)$) condition with $N\in \mathbb{N}\setminus\{1\}$ and having maximum volume…

We consider the elliptic system of linear elasticity with bounded measurable coefficients in a domain where the second Korn inequality holds. We construct heat kernel of the system subject to Dirichlet, Neumann, or mixed boundary condition…

The purpose of this article is to establish regularity and pointwise upper bounds for the (relative) fundamental solution of the heat equation associated to the weighted dbar-operator in $L^2(C^n)$ for a certain class of weights. The…

On a doubling metric measure space endowed with a "carr\'e du champ", we consider $L^p$ estimates $(G_p)$ of the gradient of the heat semigroup and scale-invariant $L^p$ Poincar\'e inequalities $(P_p)$. We show that the combination of…

We obtain heat kernel estimates for a class of fourth order non-uniformly elliptic operators in two dimensions. Contrary to existing results, the operators considered have symbols that are not strongly convex. This rises certain…

We give a simple proof of a lower bound for the Dirichlet heat kernel in terms of the Gaussian heat kernel. Using this we establish a non-existence result for semilinear heat equations with zero Dirichlet boundary conditions and initial…

Let $\Delta$ be the Laplace--Beltrami operator acting on a non-doubling manifold with two ends $\mathbb R^m \sharp \mathcal R^n$ with $m > n \ge 3$. Let $\frak{h}_t(x,y)$ be the kernels of the semigroup $e^{-t\Delta}$ generated by $\Delta$.…

We adapt in the present note the perturbation method introduced in [3] to get a Gaussian lower bound for the Neumann heat kernel of the Laplace-Beltrami operator on an open subset of a compact Riemannian manifold.

The aim of this paper is to construct (explicit) heat kernels for some hybrid evolution equations which arise in physics, conformal geometry and subelliptic PDEs. Hybrid means that the relevant partial differential operator appears in the…

We study the geometry associated to the Grusin operator G=\Delta_{x}+|x|^{2}\partial_{u}^{2} on \mathbb{R}_{x}^{n}\times\mathbb{R}_{u}, to obtain heat kernel estimates for this operator. The main work is to find the shortest geodesics…

We consider continuous time simple random walks with arbitrary speed measure $\theta$ on infinite weighted graphs. Write $p_t(x,y)$ for the heat kernel of this process. Given on-diagonal upper bounds for the heat kernel at two points…

In this paper, we first derive a Sobolev inequality along the harmonic-Ricci flow. We then prove a linear parabolic estimate based on the Sobolev inequality and Moser's iteration. As an application, we will obtain an upper bound estimate…

Let $(M^m,g)$ be a m-dimensional complete Riemannian manifold which satisfies the n-Sobolev inequality and on which the volume growth is comparable to the one of $\R^n$ for big balls; if the Hodge Laplacian on 1-forms is strongly positive…

We consider a class of fourth order uniformly elliptic operators in planar Euclidean domains and study the associated heat kernel. For operators with $L^{\infty}$ coefficients we obtain Gaussian estimates with best constants, while for…

Let $m\in\mathbb N$, $P(D):=\sum_{|\alpha|=2m}(-1)^m a_\alpha D^\alpha$ be a $2m$-order homogeneous elliptic operator with real constant coefficients on $\mathbb{R}^n$, and $V$ a measurable function on $\mathbb{R}^n$. In this article, the…