相关论文: Diffusion in small time in incomplete sub-Riemanni…

In this article we derive moment estimates, exponential integrability, concentration inequalities and exit times estimates for canonical diffusions in two settings each beyond the scope of Riemannian geometry. Firstly, we consider…

Let M be a complete Riemannian manifold with a free cocompact Z^k-action. Let k(t,x,y) be the heat kernel on M. We compute the asymptotics of k(t,x,y) in the limit in which t goes to infinity and d(x,y) is comparable to sqrt{t}. We show…

A new type of gradient estimate is established for diffusion semigroups on non-compact complete Riemannian manifolds. As applications, a global Harnack inequality with power and a heat kernel estimate are derived for diffusion semigroups on…

We give sharp conditions for the large time asymptotic simplification of aggregation-diffusion equations with linear diffusion. As soon as the interaction potential is bounded and its first and second derivatives decay fast enough at…

We study a system of $n$ differential equations, each in dimension $d$. Only the first equation is forced by a Brownian motion and the dependence structure is such that, under a local weak H\"ormander condition, the noise propagates to the…

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…

The main results of this article are small time heat comparison results for two points in two manifolds with characteristic functions as initial temperature distributions (Theorems 1 and 2). These results are based on the geometric concepts…

We show a diffusive upper bound on the transition probability of a tagged particle in the symmetric simple exclusion process. The proof relies on optimal spectral gap estimates for the dynamics in finite volume, which are of independent…

Let $\Omega$ be an open set in a complete, smooth, non-compact, $m$-dimensional Riemannian manifold $M$ without boundary, where $M$ satisfies a two-sided Li-Yau gaussian heat kernel bound. It is shown that if $\Omega$ has infinite measure,…

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…

On a complete non-compact Riemannian manifold satisfying the volume doubling property, we give conditions on the negative part of the Ricci curvature that ensure that, unless there are harmonic one-forms, the Gaussian heat kernel upper…

We derive large time upper bounds for heat kernels on vector bundles of differential forms on a class of non-compact Riemannian manifolds under certain curvature conditions.

Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…

Given a domain $\Omega$ of a complete Riemannian manifold $\mathcal{M}$ and define $\mathcal{A}$ to be the Laplacian with Neumann boundary condition on $\Omega$. We prove that, under appropriate conditions, the corresponding heat kernel…

We establish two-sided Gaussian bounds on the heat kernel of divergence-form parabolic equation with singular time-inhomogeneous vector field satisfying some minimal assumptions.

For the sake of computational efficiency and for theoretical purposes, in mathematical modelling, the Dirac Delta distributions are often utilized as a replacement for cells or vesicles, since the size of cells or vesicles is much smaller…

We consider a diffusion problem on a network on whose nodes we impose Dirichlet and generalized, non-local Kirchhoff-type conditions. We prove well-posedness of the associated initial value problem, and we exploit the theory of…

We consider a complete noncompact smooth Riemannian manifold $M$ with a weighted measure and the associated drifting Laplacian. We demonstrate that whenever the $q$-Bakry-\'Emery Ricci tensor on $M$ is bounded below, then we can obtain an…

We prove global Sobolev regularity and pointwise upper bounds for the gradient of transition densities associated with second order differential operators in $\mathbb{R}^d$ with unbounded diffusion, drift and potential terms.

Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on $\mathbb{R}^n$. In particular, in the case when $n=2$ they obtained Gaussian…