Related papers: Heat kernels for non-symmetric diffusion operators…

In this paper we investigate the existence and uniqueness of weak solutions for kinetic stochastic differential equations with H\"older diffusion and unbounded singular drifts in Kato's class. Moreover, we also establish sharp two-sided…

In this work, we study the existence and nonexistence of nonnegative solutions to a class of nonlocal elliptic systems set in a bounded open subset of $\mathbb{R}^N$. The diffusion operators are of type $u_i\mapsto d_i(-\Delta)^{s_i}u_i$…

We provide pointwise upper bounds for the transition kernels of semigroups associated with a class of systems of nondegenerate elliptic partial differential equations with unbounded coefficients with possibly unbounded diffusion…

We consider the heat equation $u_t=Lu$ where $L$ is a second-order difference operator in a discrete variable $n$. The fundamental solution has an expansion in terms of the Bessel functions of imaginary argument. The coefficients…

We prove upper and lower bounds of the heat kernel for the operator $\Delta-\nabla (\frac{1}{|x|^{\alpha}})\cdot \nabla $ in $\mathbb{R}^{n}\setminus\{0} $ where $\alpha >0$. We obtain these bounds from an isoperimetric inequality for a…

Permutation invariance is fundamental in molecular point-cloud generation, yet most diffusion models enforce it indirectly via permutation-equivariant networks on an ordered space. We propose to model diffusion directly on the quotient…

We construct the heat kernel on curvilinear polygonal domains in arbitrary surfaces for Dirichlet, Neumann, and Robin boundary conditions as well as mixed problems, including those of Zaremba type. We compute the short time asymptotic…

We give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet condition for a general class of domains including Lipschitz domains.

We present a brief overview of several approaches for calculating the local asymptotic expansion of the heat kernel for Laplace-type operators. The different methods developed in the papers of both authors some time ago are described in…

This paper presents a complete analysis of the observability property of heat equations with time-dependent real analytic memory kernels. More precisely, we characterize the geometry of the space-time measurable observation sets ensuring…

We calculate the heat-kernel coefficients, up to $a_2$, for a U(1) bundle on the 4-Ball for boundary conditions which are such that the normal derivative of the field at the boundary is related to a first-order operator in boundary…

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…

In this paper, we derive explicit sharp two-sided estimates for the Dirichlet heat kernels of a large class of symmetric (but not necessarily rotationally symmetric) L\'evy processes on half spaces for all $t>0$. These L\'evy processes may…

Networks constitute fundamental organizational structures across biological systems, although conventional graph-theoretic analyses capture exclusively pairwise interactions, thereby omitting the intricate higher-order relationships that…

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 consider a class of homogeneous partial differential operators on a finite-dimensional vector space and study their associated heat kernels. The heat kernels for this general class of operators are seen to arise naturally as the limiting…

A diagramatic heat kernel expansion technique is presented. The method is especially well suited to the small-derivative expansion of the heat kernel, but it can also be used to reproduce the results obtained by the approach known as…

We consider a large class of symmetric pure jump Markov processes dominated by isotropic unimodal L\'evy processes with weak scaling conditions. First, we establish sharp two-sided heat kernel estimates for these processes in $C^{1,1}$ open…

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.

In this paper, we study Ornstein-Uhlenbeck operators with quadratic potentials. We use Hamiltonian formalism to characterise the singularities produced by the potentials by finding explicit geodesics of the operators, and obtain the heat…