相关论文: Robust near-diagonal Green function estimates

The paper deals with point-wise estimates for the heat kernel of a nonlocal convolution type operator with a kernel that decays at least exponentially at infinity. It is shown that the large time behaviour of the heat kernel depends…

For the $\alpha$-Green kernel $g^\alpha_D$ on a domain $D\subset\mathbb R^n$, $n\geqslant2$, associated with the $\alpha$-Riesz kernel $|x-y|^{\alpha-n}$, where $\alpha\in(0,n)$ and $\alpha\leqslant2$, and a relatively closed set $F\subset…

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…

We obtain two-sided heat kernel estimates for Riemannian manifolds with ends with mixed boundary condition, provided that the heat kernels for the ends are well understood. These results extend previous results of Grigor'yan and…

We have constructed a sequence of solutions of the Helmholtz equation forming an orthogonal sequence on a given surface. Coefficients of these functions depend on an explicit algebraic formulae from the coefficient of the surface. Moreover,…

We prove a sharp uniform generalized Gaussian bound for the Green's function of the Lax-Wendroff and Beam-Warming schemes. Our bound highlights the spatial region that leads to the well-known (rather weak) instability of these schemes in…

Working within the framework of the covariant perturbation theory, we obtain the coincidence limit of the heat kernel of an elliptic second order differential operator that is applicable to a large class of quantum field theories. The basis…

We verify a conjecture proposed by X. Chen and Y. Shi, which arises from their study of the Green function on spheres in Euclidean space. More precisely, let $M\subset \mathbb{R}^3$ be a closed $C^{2}$ embedded surface and suppose that…

A general technique is developed for calculating functional determinants of second-order differential operators with Dirichlet, periodic, and antiperiodic boundary conditions. As an example, we give simple formulas for a harmonic oscillator…

The quasiclassical Green functions of the Dirac and Klein-Gordon equations in the external electric field are obtained with the first correction taken into account. The relevant potential is assumed to be localized, while its spherical…

Our main aim is to study Green function for the fractional Hardy operator $P:=(-\Delta)^s -\frac{\theta}{|x|^{2s}}$ in $\mathbb{R}^N$, where $0<\theta<\Lambda_{N,s}$ and $\Lambda_{N,s}$ is the best constant in the fractional Hardy…

In this paper, we derive sharp two side heat kernel estimate on exterior $C^{1,1}$ domains in the plane, and sharp upper heat kernel bound on exterior $C^{1,\mathrm{Dini}}$ domains in $\mathbb{R}^n$, $n\ge 2$. Estimates for Green's function…

Asymptotic formulae for Green's kernels $G_\epsilon({\bf x}, {\bf y})$ of various boundary value problems for the Laplace operator are obtained in regularly perturbed domains and certain domains with small singular perturbations of the…

In this paper we study optimal lower and upper bounds for functionals involving the first Dirichlet eigenvalue $\lambda_{F}(p,\Omega)$ of the anisotropic $p$-Laplacian, $1<p<+\infty$. Our aim is to enhance how, by means of the $\mathcal…

Let $M$ be a complete non-compact Riemannian manifold and $\sigma $ be a Radon measure on $M$, we study the existence and non-existence of positive solutions to a nonlocal elliptic inequality \begin{equation*} (-\Delta)^{\alpha} u\geq…

Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic…

In this paper, new representations of the Green's function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of the new representation are: a) in addition to additive terms…

We consider supergravity configuration of D5 branes wrapped on supersymmetric 2-cycles and use it to calculate one-point and two-point Green functions of some special operators in N=2 super Yang-Mills theory. We show that Green functions…

We consider heat kernel for higher-order operators with constant coefficients in $d$-dimensio\-nal Euclidean space and its asymptotic behavior. For arbitrary operators which are invariant with respect to $O(d)$-rotations we obtain exact…

We study the Green function gr_\Gamma\ for the Laplace operator on the quotient of the hyperbolic plane by a cofinite Fuchsian group \Gamma. We use a limiting procedure, starting from the resolvent kernel, and lattice point estimates for…