Related papers: Dirichlet heat kernel estimates of subordinate dif…

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…

This paper is devoted to the study of the one dimensional non homogeneous heat equation coupled to Dirichlet Boundary Conditions. We obtain the explicit expression of the solution of the linear equation by means of a direct integral in an…

We present a novel approach of discretizing variable coefficient diffusion operators in the context of meshfree generalized finite difference methods. Our ansatz uses properties of derived operators and combines the discrete Laplace…

We establish sharp pointwise estimates for the ground states of some singular fractional Schr\"odinger operators on relatively compact Euclidean subsets. The considered operators are of the type $(-\Delta)^{\alpha/2}|_\Om-c|x|^{-\alpha}$,…

We consider the formal SDE dX t = b(t, X t)dt + dZ t , X 0 = x $\in$ R d , (E) where b $\in$ L r ([0, T ], B $\beta$ p,q (R d , R d)) is a time-inhomogeneous Besov drift and Z t is a symmetric d-dimensional $\alpha$-stable process, $\alpha$…

Smoothing a signal based on local neighborhoods is a core operation in machine learning and geometry processing. On well-structured domains such as vector spaces and manifolds, the Laplace operator derived from differential geometry offers…

We give matching upper and lower bounds for the Dirichlet heat kernel of a Schr\"odinger operator $\Delta+W$ in the domain above the graph of a bounded Lipschitz function, in the case when $W$ decays away from the boundary faster than…

Let $\alpha\in(0,2)$ and $d\in{\mathbb N}$. Consider the following SDE in ${\mathbb R}^d$:$${\rm d}X_t=b(t,X_t){\rm d} t+a(t,X_{t-}){\rm d} L^{(\alpha)}_t,\ \ X_0=x,$$where $L^{(\alpha)}$ is a $d$-dimensional rotationally invariant…

This paper is devoted to the study of gradient estimates for the Dirichlet problem of the heat equation in the exterior domain of a compact set. Our results describe the time decay rates of the derivatives of solutions to the Dirichlet…

We present a very quick and powerful method for the calculation of heat-kernel coefficients. It makes use of rather common ideas, as integral representations of the spectral sum, Mellin transforms, non-trivial commutation of series and…

By making full use of heat kernel estimates, we establish the integral tests on the zero-one laws of upper and lower bounds for the sample path ranges of symmetric Markov processes. In particular, these results concerning on upper rate…

We consider Dirichlet heat kernel $p_a^{(\mu)}(t,x,y)$ for the Bessel differential operator $L^{(\mu)}=\frac{d^2}{dx^2}+\frac{2\mu+1}{2x}$, $\mu\in\mathbb{R}$, in half-line $(a,\infty)$, $a>0$, and provide its asymptotic expansions for…

This paper considers the properties of Dirichlet Spaces of Homogeneous type which consist of band limited functions that are nearly exponential localizations on $\mathbb{R}^k.$ This is a powerful tool in harmonic analysis and it makes…

We investigate selfadjoint positivity preserving $C_0$-semigroups that are dominated by the free heat semigroup on $\mathbb R^d$. Major examples are semigroups generated by Dirichlet Laplacians on open subsets or by Schr\"odinger operators…

A subordinate Brownian motion is a L\'evy process which can be obtained by replacing the time of the Brownian motion by an independent subordinator. The infinitesimal generator of a subordinate Brownian motion is $-\phi(-\Delta)$, where…

In this paper we study pseudo-processes related to odd-order heat-type equations composed with L\'evy stable subordinators. The aim of the article is twofold. We first show that the pseudo-density of the subordinated pseudo-process can be…

In this paper, we derive sharp two side heat kernel estimate on exterior $C^{1,1}$ domains in the plane, and sharp upper heat kernel bound on exterior $C^{1,\mathrm{Dini}}$ domains in $\mathbb{R}^n$, $n\ge 2$. Estimates for Green's function…

For given strongly local Dirichlet forms with possibly degenerate symmetric (sub)-elliptic matrix, we show the existence of weak solutions to the stochastic differential equations (associated with the Dirichlet forms) starting from all…

This paper considers the Dirichlet problem $$ -\mathrm{div}(a\nabla u_a)=f \quad \hbox{on}\,\,\ D, \qquad u_a=0\quad \hbox{on}\,\,\partial D, $$ for a Lipschitz domain $D\subset \mathbb R^d$, where $a$ is a scalar diffusion function. For a…

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…