Related papers: The Green function estimates for strongly elliptic…
A uniform gradient for functions u which satisfy a system of N second-order partial differential inequalities is given in this paper. Some structure conditions are given for the coefficients of the matrices of second-order terms and of…
We establish the existence and the pointwise bound of the fundamental solution for the stationary Stokes system with measurable coefficients in the whole space $\mathbb{R}^d$, $d \ge 3$, under the assumption that weak solutions of the…
For a family of second-order elliptic systems in divergence form with rapidly oscillating almost-periodic coefficients, we obtain estimates for approximate correctors in terms of a function that quantifies the almost periodicity of the…
In three-dimensional case, we consider two classical operators: Schrodinger operator and an operator in the divergence form. For slowly-decaying oscillating potentials, we establish spatial asymptotics of the Green's function. The main term…
For a given second order elliptic operation $\mathcal{L}$ in a domain $\Omega\subset{\mathbb{R}}^\mathbf{N}$, $\mathbf{N}\ $, and a compact set $\mathbf{K}\subset\Omega$, order $\mathbf{N}$-$2$-Ahlfors-David regular, we define the space…
In this work we develop an algebraic theory of linear recurrence equations and systems with constant coefficients and reflection. We obtain explicit solutions and the Green's functions associated to different problems under general linear…
Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of…
The well-known Green's function method has been recently generalized to nonlinear second order differential equations. In this paper we study possibilities of exact Green's function solutions of nonlinear differential equations of higher…
We study questions related to critical points of the Green's function of a bounded multiply connected domain in the complex plane. The motion of critical points, their limiting positions as the pole approaches the boundary and the…
We describe the computation of generalized Green functions and 2-parameter Green functions for finite reductive groups.
In this paper we will show several properties of the Green's functions related to various boundary value problems of arbitrary even order. In particular, we will write the expression of the Green's functions related to the general…
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.
We consider a divergence-form elliptic difference operator on the lattice $\mathbb{Z}^d$, with a coefficient matrix that is an i.i.d. perturbation of the identity matrix. Recently, Bourgain introduced novel techniques from harmonic analysis…
Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…
It is well known that second order homogeneous linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation underlies the Liouville-Green method and many other techniques for…
In this work we revise the most recent developments concerning the study of first order problems regarding differential equations with involutions. We take into account two cases: the case of initial conditions and constant coefficients and…
We deal with boundary value problems for second-order nonlinear elliptic equations in divergence form, which emerge as Euler-Lagrange equations of integral functionals of the Calculus of Variations built upon possibly anisotropic norms of…
We define a non-local gauge-invariant Green's function which can distinguish between the symmetric (confinement) and broken (Higgs) phases of the hot SU(2)xU(1) electroweak theory to all orders in the perturbative expansion. It is related…
We extend the upper estimates obtained by M. Carlehed and B.-Y. Chen about the ratio of the classical and pluricomplex Green functions to the case of $\mathcal C^2$-smooth locally $\mathbb C$-convexifiable domains of finite type. We also…
In calculating Green functions for interacting quantum systems numerically one often has to resort to finite systems which introduces a finite size level spacing. In order to describe the limit of system size going to infinity correctly,…