Related papers: Genuinely sharp estimates for heat kernels on Weyl…

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…

Various sharp pointwise estimates for the gradient of solutions to the heat equation are obtained. The Dirichlet and Neumann conditions are prescribed on the boundary of a half-space. All data belong to the Lebesgue space $L^p$. Derivation…

In this paper, we derive explicit sharp two-sided estimates of the Dirichlet heat kernels for a class of symmetric subordinate diffusion processes with diffusive components in $C^{1, \alpha}(\alpha\in (0, 1])$ open sets in $\mathbb R^d$…

We consider the heat-kernel expansion of the massive Laplace operator on the three dimensional ball with Dirichlet boundary conditions. Using this example, we illustrate a very effective scheme for the calculation of an (in principle)…

This paper presents a detailed analysis of the heat kernel on an $(\mathbb{N}\times\mathbb{N})$-parameter family of compact metric measure spaces, which do not satisfy the volume doubling property. In particular, uniform bounds of the heat…

We study Schroedinger operators with Robin boundary conditions on exterior domains in $\R^d$. We prove sharp point-wise estimates for the associated semi-groups which show, in particular, how the boundary conditions affect the time decay of…

Using sharp global heat kernel bounds and geodesic comparison geometry, we show that the Dalang condition for well-posedness of the parabolic Anderson model with measure-valued initial conditions, first introduced on Euclidean space, holds…

For $d\geq 2$, we establish the existence and uniqueness of heat kernels for a large class of time-dependent second order diffusion operator with jumps, which is the sum of time-dependent of a second order elliptic differential operators…

We prove genuinely sharp estimates for the Jacobi heat kernels introduced in the context of the multidimensional cone $\mathbb{V}^{d+1}$ and its surface $\mathbb{V}^{d+1}_0$. To do so, we combine the theory of Jacobi polynomials on the cone…

We study reflected jump diffusions on Ahlfors regular domains in general metric measure spaces. Under the condition that the Dirichlet form on the ambient space satisfies a capacity upper bound estimate, we construct an extension operator…

We investigate heat kernel estimates of the form $p_{t}(x, x)\geq c_{x}t^{-\alpha},$ for large enough $t,$ where $\alpha$ and $c_{x}$ are positive reals and $c_{x}$ may depend on $x,$ on manifolds having at least one end.

We establish global two-sided heat kernel estimates (for full time and space) of the Schr\"odinger operator $-\frac{1}{2}\Delta+V$ on $\R^d$, where the potential $V(x)$ is locally bounded and behaves like $c|x|^{-\alpha}$ near infinity with…

We give sharp asymptotic estimates at infinity of all radial partial derivatives of the heat kernel on H-type groups. As an application, we give a new proof of the discreteness of the spectrum of some natural sub-Riemannian…

We study entire solutions of the biharmonic heat equation on complete Riemannian manifolds without boundary. We provide exponential decay estimates for the biharmonic heat kernel under assumptions on the lower bound of Ricci curvature and…

Let $(X,g)$ be a product cone with the metric $g=dr^2+r^2h$, where $X=C(Y)=(0,\infty)_r\times Y$ and the cross section $Y$ is a $(n-1)$-dimensional closed Riemannian manifold $(Y,h)$. We study the upper boundedness of heat kernel associated…

Being motivated by applications to the physics of Weyl semimetals we study spectral geometry of Dirac operator with an abelian gauge field and an axial vector field. We impose chiral bag boundary conditions with variable chiral phase…

In the paper we consider the Bessel differential operator L^(\mu)=\dfrac{d^2}{dx^2}+\dfrac{2\mu+1}{x}\dfrac{d}{dx} in half-line (a,\infty), a>0, and its Dirichlet heat kernel p_a^(\mu)(t,x,y). For \mu=0, by combining analytical and…

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…

In this article, we conjecture exact estimates for the Weyl-invariant Opdam-Cherednik hypergeometric functions. We prove the conjecture for the root system $A_n$ and for all rank 1 cases. We provide other evidence that the conjecture might…

We consider metric graphs with Kirchhoff boundary conditions. We study the intrinsic metric, volume doubling and a Poincar\'e inequality. This enables us to prove a parabolic Harnack inequality. The proof involves various techniques from…