Related papers: Heat kernel estimates for Dirichlet forms degenera…

We provide sharp two-sided estimates of the Fourier-Bessel heat kernel and we give sharp two-sided estimates of the transition probability density for the Bessel process in (0,1) killed at 1 and killed or reflected at 0.

We give two-sided, global (in all variables) estimates of the heat kernel and the Green function of the fractional Schr\"odinger operator with a non-negative and locally bounded potential $V$ such that $V(x) \to \infty$ as $|x| \to \infty$.…

In this paper we consider a time-continuous random walk in $\mathbb{Z}^d$ in a dynamical random environment with symmetric jump rates to nearest neighbours. We assume that these random conductances are stationary and ergodic and, moreover,…

The aim of this paper is threefold. First, we obtain the precise bounds for the heat kernel on isotropic Heisenberg groups by using well-known results in the three dimensional case. Second, we study the asymptotic estimates at infinity for…

We prove heat kernel bounds for the operator (1 + |x|^{\alpha})\Delta in R^N, through Nash inequalities and weighted Hardy inequalities.

We prove a boundary Harnack inequality for jump-type Markov processes on metric measure state spaces, under comparability estimates of the jump kernel and Urysohn-type property of the domain of the generator of the process. The result holds…

We give two-term small-time approximation for the trace of the Dirichlet heat kernel of bounded smooth domain for unimodal L\'evy processes satisfying the weak scaling conditions.

Let $(\mathbb M, d,\mu)$ be a metric measure space with upper and lower densities: $$ \begin{cases} |||\mu|||_{\beta}:=\sup_{(x,r)\in \mathbb M\times(0,\infty)} \mu(B(x,r))r^{-\beta}<\infty;\\ |||\mu|||_{\beta^{\star}}:=\inf_{(x,r)\in…

We provide sharp two-sided estimates on the Dirichlet heat kernel $k_1(t,x,y)$ for the Laplacian in a ball. The result accurately describes the exponential behaviour of the kernel for small times and significantly improves the qualitatively…

When studying non-symmetric nonlocal operators $$ {\cal L} f(x) = \int_{{\bf R}^d} \left( f(x+z)-f(x)-\nabla f(x)\cdot z 1_{\{|z|\leq 1\}} \right) \frac{\kappa (x, z)}{|z|^{d+\alpha}} d z , $$ where $0<\alpha<2$ and $\kappa (x, z)$ is a…

We present on-diagonal heat kernel estimates and quantitative homogenization statements for the one-dimensional Bouchaud trap model. The heat kernel estimates are obtained using standard techniques, with key inputs coming from a careful…

The formulation of gauge theories on compact Riemannian manifolds with boundary leads to partial differential operators with Gilkey--Smith boundary conditions, whose peculiar property is the occurrence of both normal and tangential…

In this paper we consider a large class of symmetric Markov processes $X=(X_t)_{t\ge0}$ on $\R^d$ generated by non-local Dirichlet forms, which include jump processes with small jumps of $\alpha$-stable-like type and with large jumps of…

Let $L$ be an elliptic differential operator on a complete connected Riemannian manifold $M$ such that the associated heat kernel has two-sided Gaussian bounds as well as a Gaussian type gradient estimate. Let $L^{(\aa)}$ be the…

We prove qualitatively sharp heat kernel bounds in the setting of Fourier-Bessel expansions when the associated type parameter $\nu$ is half-integer. Moreover, still for half-integer $\nu$, we also obtain sharp estimates of all kernels…

The worldline formalism has in recent years emerged as a powerful tool for the computation of effective actions and heat kernels. However, implementing nontrivial boundary conditions in this formalism has turned out to be a difficult…

We obtain sharp estimates for the Jacobi heat kernel in a range of parameters where the result has not been established before. This extends and completes an earlier result due to the authors. The proof is based on a generalization of the…

Let $\alpha(x)$ be a measurable function taking values in $ [\alpha_1,\alpha_2]$ for $0<\A_1\le \A_2<2$, and $\kappa(x,z)$ be a positive measurable function that is symmetric in $z$ and bounded between two positive constants. Under a…

The first heat kernel coefficients are calculated for a dispersive ball whose permittivity at high frequency differs from unity by inverse powers of the frequency. The corresponding divergent part of the vacuum energy of the electromagnetic…

In this work we construct the heat kernel of the 1/2-order Laplacian perturbed by the first-order gradient term in H\"older space and the zero-order potential term in generalized Kato's class, and obtain sharp two-sided estimates as well as…