Related papers: Regularity for parabolic equations with singular n…

We prove that in presence of $L^2$ Gaussian estimates, so-called Davies-Gaffney estimates, on-diagonal upper bounds imply precise off-diagonal Gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces.

We prove a variant of the Davies-Gaffney-Grigor'yan Lemma for the continuous time heat kernel on graphs. We use it together with the Li-Yau inequality to obtain strong heat kernel estimates for graphs satisfying the exponential curvature…

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…

In this work, we consider solutions to (fully nonlinear) parabolic integro-differential equations with integrable interaction kernels. A typical equation would be that obtained by starting with, for $s\in(0,1)$, the $s$-fractional heat…

Two-sided Gaussian estimates for the fundamental solution of a second order linear parabolic differential equation are upper and lower bounds in terms of the fundamental solution of the classical heat conduction equation. In his seminal…

We apply the Davies method to prove that for any regular Dirichlet form on a metric measure space, an off-diagonal stable-type upper bound of the heat kernel is equivalent to the conjunction of the on-diagonal upper bound, a cutoff…

We adapt in the present note the perturbation method introduced in [3] to get a Gaussian lower bound for the Neumann heat kernel of the Laplace-Beltrami operator on an open subset of a compact Riemannian manifold.

The heat-balance integral method of Goodman has been thoroughly analyzed in the case of a parabolic profile with unspecified exponent depending on the boundary condition imposed. That the classical Good man's boundary conditions defining…

A class of inverse problems for a heat equation with involution perturbation is considered using four different boundary conditions, namely, Dirichlet, Neumann, periodic and anti-periodic boundary conditions. Proved theorems on existence…

In the context of a metric measure Dirichlet space satisfying volume doubling and Poincar\'e inequality, we prove the parabolic Harnack inequality for weak solutions of the heat equation associated with local nonsymmetric bilinear forms. In…

We investigate the equivalence of Sobolev inequalities and the conjunction of Gaussian upper heat kernel bounds and volume doubling on large scales on graphs. For the normalizing measure, we obtain their equivalence up to constants by…

In the sub-Riemannian manifolds, on the one hand, following Baudoin-Garofalo \cite{BaudoinGarofalo}, the upper bound for heat kernels associated to a class of locally subelliptic operators are given under the generalized curvature-dimension…

We prove a bound on the heat trace of the Neumann Laplacian on a convex domain that captures the first two terms in its small-time expansion, but is valid for all times and depends on the underlying domain only through very simple geometric…

Let $(M^m,g)$ be a m-dimensional complete Riemannian manifold which satisfies the n-Sobolev inequality and on which the volume growth is comparable to the one of $\R^n$ for big balls; if the Hodge Laplacian on 1-forms is strongly positive…

We establish sharp two-sided bounds on the heat kernel of the fractional Laplacian, perturbed by a drift having critical-order singularity, by transferring it to appropriate weighted space with singular weight.

We prove Calder\'on-Zygmund type estimates of weak solutions to non-homogeneous nonlocal parabolic equations under a minimal regularity requirement on kernel coefficients. In particular, the right-hand side is presented by a sum of…

We construct the fundamental solution of second order parabolic equations in non-divergence form under the assumption that the coefficients are of Dini mean oscillation in the spatial variables. We also prove that the fundamental solution…

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…

The heat kernel method is extended to the case of finite temperature. Special emphasis is given to the study of gauge theories. Due to the compactness of space in the Euclidean time direction (inverse temperature) the field strength cannot…

We prove sharp two-sided bounds of the fundamental solution for an integro-differential operator of order $\alpha \in (0,2)$ that generates a $d$-dimensional Markov process. The corresponding Dirichlet form is comparable to that of $d$…