Related papers: Comments on the Green's function of a planar domai…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
The Green's functions for the Laplace equation respectively satisfying the Dirichlet and Neumann boundary conditions on the upper side of an infinite plane with a circular hole are introduced and constructed. These functions enables…
Homogeneous and inhomogeneous biharmonic equation are considered on the $n$-dimensional unit sphere. The Green function is given as a series of Gegenbauer polynomials. In the paper, explicit representations of the Green function are found…
Using the logarithmic capacity, we give quantitative estimates of the Green function, as well as lower bounds of the Bergman kernel for bounded pseudoconvex domains in $\mathbb C^n$ and the Bergman distance for bounded planar domains. In…
We report on the passive measurement of time-dependent Green's functions in the optical frequency domain with low-coherence interferometry. Inspired by previous studies in acoustics and seismology, we show how the correlations of a…
We derive equations of motion for higher order density response functions using the theory of thermodynamic Green's functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions.…
It has been known for some time that the Green's function of a planar domain can be defined in terms of the exit time of Brownian motion, and this definition has been extended to stopping times more general than exit times. In this paper,…
A domain integral method employing a specific Green's function (i.e., incorporating some features of the global problem of wave propagation in an inhomogeneous medium) is developed for solving direct and inverse scattering problems relative…
Green's function plays a significant role in both theoretical analysis and numerical computing of partial differential equations (PDEs). However, in most cases, Green's function is difficult to compute. The troubles arise in the following…
We give some remarks on some manifolds K3 surfaces, Complex projective spaces, real projective space and Torus and the classification of two dimensional Riemannian surfaces, Green functions and the Stokes formula. We also, talk about traces…
A method to calculate exact Green's functions on lattices in various dimensions is presented. Expressions in terms of generalized hypergeometric functions in one or more variables are obtained for various examples by relating the resolvent…
We construct Green functions of conormal derivative problems for the stationary Stokes system with measurable coefficients in a two dimensional Reifenberg flat domain.
Let $L$ be a second-order, homogeneous, constant (complex) coefficient elliptic system in ${\mathbb{R}}^n$. The goal of this article is provide a qualitative and quantitative study of the nature of the Green function associated with the…
We develop a general technique for computing functional integrals with fixed area and boundary length constraints. The correct quantum dimensions for the vertex functions are recovered by properly regularizing the Green function. Explicit…
This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…
We show that Green functions of second-order differential operators with singular or unbounded coefficients can have an anomalous behaviour in comparison to the well-known properties of Green functions of operators with bounded…
We show how few-particle Green's functions can be calculated efficiently for models with nearest-neighbor hopping, for infinite lattices in any dimension. As an example, for one dimensional spinless fermions with both nearest-neighbor and…
A model of a quantum dot with impurity in the Lobachevsky plane is considered. Relying on explicit formulae for the Green function and the Krein $Q-$function which have been derived in a previous work we focus on the numerical analysis of…
We study ($p$-harmonic) singular functions, defined by means of upper gradients, in bounded domains in metric measure spaces. It is shown that singular functions exist if and only if the complement of the domain has positive capacity, and…
It is shown that the Green's function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of translation operator. Explicit examples are given for one- and two-dimensional lattices.