Related papers: Pointwise monotonicity of heat kernels
We analyze the control properties of heat equations with memory terms. We recall previous results showing that if the moving support of the control covers the whole domain where heat diffuses, the system is null controllable when the memory…
A non-relativistic quantum model is considered with a point particle carrying a charge $e$ and moving on the plane pierced by two infinitesimally thin Aharonov-Bohm solenoids and subjected to a perpendicular uniform magnetic field of…
We establish Gaussian-type upper bounds on the heat kernel for a continuous-time random walk on a graph with unbounded weights under an ergodicity assumption. For the proof we use Davies' perturbation method, where we show a maximal…
We obtain an upper heat kernel bound for the Laplacian on metric graphs arising as one skeletons of certain polygonal tilings of the plane, which reflects the one dimensional as well as the two dimensional nature of these graphs.
In this paper characterizations of graphs satisfying heat kernel estimates for a wide class of space-time scaling functions are given. The equivalence of the two-sided heat kernel estimate and the parabolic Harnack inequality is also shown…
We study pointwise and $L^p$ gradient estimates of the heat kernel, on manifolds that may have some amount of negative Ricci curvature, provided it is not too negative (in an integral sense) at infinity. We also prove uniform boundedness…
We explore novel properties of the biharmonic heat kernel on Euclidean space and derive an entropy type quantity for the extrinsic biharmonic map heat flow which exhibits monotonicity behaviors for $n\leq 4$.
In this paper, we consider the following symmetric Dirichlet forms on a metric measure space $(M,d,\mu)$: $$\mathcal{E}(f,g) = \mathcal{E}(^{(c)}(f,g)+\int_{M\times M} (f(x)-f(y))(g(x)-g(y))\,J(dx,dy),$$ where $\mathcal{E}(^{(c)}$ is a…
On doubling metric measure spaces endowed with a strongly local regular Dirichlet form, we show some characterisations of pointwise upper bounds of the heat kernel in terms of global scale-invariant inequalities that correspond respectively…
Wavelet bases and frames consisting of band limited functions of nearly exponential localization on Rd are a powerful tool in harmonic analysis by making various spaces of functions and distributions more accessible for study and…
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…
This paper provides explicit pointwise formulas for the heat kernel on compact metric measure spaces that belong to a $(\mathbb{N}\times\mathbb{N})$-parameter family of fractals which are regarded as projective limits of metric measure…
We suggest a method of reduction of mixed absolute and relative boundary conditions to pure ones. The case of rank two tensor is studied in detail. For four-dimensional disk the corresponding heat kernel is expressed in terms of scalar heat…
We obtain Gaussian upper bounds for heat kernels of higher order differential operators with Dirichlet boundary conditions on bounded domains in $\R^N$. The bounds exhibit explicitly the nature of the spatial decay of the heat kernel close…
This article considers nonlocal heat flows into a singular target space. The problem is the parabolic analogue of a stationary problem that arises as the limit of a singularly perturbed elliptic system. It also provides a gradient flow…
In this paper we establish the existence and uniqueness of heat kernels to a large class of time-inhomogenous non-symmetric nonlocal operators with Dini's continuous kernels. Moreover, quantitative estimates including two-sided estimates,…
We study heat kernel estimates for symmetric pure jump processes on general metric measure spaces. Building on recent progress in the local setting due to S.~Eriksson-Bique, we develop a non-local version of the Whitney blending technique…
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.
Using the Zwanzig projection-operator formalism, we derive a causal two-point spatiotemporal kernel for heat conduction, defined microscopically as a space-resolved equilibrium heat-flux time-correlation function, that encodes temporal…
In this paper, we prove pointwise convergence of heat kernels for mGH-convergent sequences of $RCD^*(K,N)$-spaces. We obtain as a corollary results on the short-time behavior of the heat kernel in $RCD^*(K,N)$-spaces. We use then these…