Related papers: Heat kernel estimates for critical fractional diff…

The purpose of this article is to establish upper and lower estimates for the integral kernel of the semigroup exp(-tP) associated to a classical, strongly elliptic pseudodifferential operator P of positive order on a closed manifold. The…

We prove heat kernel estimates for the $\bar\partial$-Neumann Laplacian acting in spaces of differential forms over noncompact, strongly pseudoconvex complex manifolds with a Lie group symmetry and compact quotient. We also relate our…

We consider the heat equation associated with a class of second order hypoelliptic H\"{o}rmander operators with constant second order term and linear drift. We describe the possible small time heat kernel expansion on the diagonal giving a…

Gradient and stability type estimates of heat kernel associated with fractional power of a uniformly elliptic operator are obtained. $L^p$-operator norm of semigroups associated with fractional power of two uniformly elliptic operators are…

Let $L=-\Delta+V$ be a Schr\"odinger operator, where the potential $V$ belongs to the reverse H\"older class. By the subordinative formula, we introduce the fractional heat semigroup $\{e^{-t{L}^\alpha}\}_{t>0}, \alpha>0$, associated with…

We study the heat kernel of the supercritical fractional diffusion equation with the drift in the critical H\"{o}lder space. We show that such a drift can have point irregularities strong enough to make the heat kernel vanish at a point for…

We give local in time sharp two sided estimates of the heat kernel associated with the relativistic stable operator perturbed by a critical (Hardy) potential.

We present a method for the calculation of the $a_{3/2}$ heat kernel coefficient of the heat operator trace for a partial differential operator of Laplace type on a compact Riemannian manifold with oblique boundary conditions. Using special…

Let us consider a time-dependent differential operator quadratic with respect to the phase variables. Let us consider a multiplication operator defined with the help of a "small" matrix-valued function. Under suitable conditions, we give an…

Working within the framework of the covariant perturbation theory, we obtain the coincidence limit of the heat kernel of an elliptic second order differential operator that is applicable to a large class of quantum field theories. The basis…

We introduce a method of constructing a general Laakso space while calculating the spectrum and multiplicities of the Laplacian operator on it. Using this information, we found the leading term of the trace of the heat kernel of a Laakso…

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 construct the fundamental solution (the heat kernel) $p^{\kappa}$ to the equation $\partial_t=\mathcal{L}^{\kappa}$, where under certain assumptions the operator $\mathcal{L}^{\kappa}$ takes one of the following forms, \begin{align*}…

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…

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

In this paper we give Hamilton's Laplacian estimates for the heat equation on complete noncompact manifolds with nonnegative Ricci curvature. As an application, combining Li-Yau's lower and upper bounds of the heat kernel, we give an…

Suppose that $d\ge 1$ and $\alpha\in (0, 2)$. In this paper, by using probabilistic methods, we establish sharp two-sided pointwise estimates for the Dirichlet heat kernels of $\{\Delta+ a^\alpha \Delta^{\alpha/2}; \ a\in (0, 1]\}$ on…

We survey the recent progress in the study of heat kernels for a class of non-symmetric non-local operators. We focus on the existence and sharp two-sided estimates of the heat kernels and their connection to jump diffusions.

The heat kernel associated with the setting of the classical Jacobi polynomials is defined by an oscillatory sum which cannot be computed explicitly, in contrast to the situation for the two other classical systems of orthogonal…

We give a short overview of the effective action approach in quantum field theory and quantum gravity and describe various methods for calculation of the asymptotic expansion of the heat kernel for second-order elliptic partial differential…