Related papers: Pointwise estimates for the polyharmonic Green fun…
We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…
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 prove a sharp estimate for conjugate functions using a harmonic majorant in a half-strip. As an application, we remove the logarithmic loss from a theorem of Papadopoulos on minima of trigonometric polynomials and obtain the optimal…
We give a complete proof of the generalized Khavinson conjecture which states that, for bounded harmonic functions on the unit ball of $\mathbb{R}^n$, the sharp constants in the estimates for their radial derivatives and for their gradients…
In this paper, we give the explicit expressions of high-order Green operators on the disk and the polydisc, and hence the kernel functions of high-order Green operators are also presented. As applications, we present the explicit integral…
In this paper, we consider the set of r-symbols in a full generality. We construct Hall-Littlewood functions and Kostka functions associated to those r-symbols. We also discuss a multi-parameter version of those functions. We show that…
We prove a Pucci-Serrin conjecture on critical dimensions under a uniform bound on the energy. The method is based on the analysis of the Green's function of polyharmonic operators with "almost" Hardy potential.
We study several classes of isolated singularities of plurisubharmonic functions that can be approximated by analytic singularities with control over their residual Monge--Amp\`ere masses. They are characterized in terms of Green functions…
In this paper, we summarize the technique of using Green functions to solve electrostatic problems. We start by deriving the electric potential in terms of a Green function and a charge distribution. We then provide a variety of example…
For positive $p$-harmonic functions on Riemannian manifolds, we derive a gradient estimate and Harnack inequality with constants depending only on the lower bound of the Ricci curvature, the dimension $n$, $p$ and the radius of the ball on…
Indecomposible semifinite harmonic functions on the direct product of graded graphs are classified. As a particular case, the full list of indecomposible traces for the infinite inverse symmetric semigroup is obtained.
In this paper, we study $(p,V)$-harmonic functions on complete Riemannian manifolds using the Moser iteration method. A volume comparison theorem and a Sobolev embedding theorem are established under the Bakry-$\acute{E}$mery curvature…
We consider in the plane the problem of reconstructing a domain from the normal derivative of its Green's function with pole at a fixed point in the domain. By means of the theory of conformal mappings, we obtain existence, uniqueness,…
Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual…
In this paper we obtain an explicit formula of the parameter dependence of the partial derivatives of the Green's functions related to two-point boundary conditions. Such expression follows as an integral of both kernels times the…
We construct examples of nonnegative harmonic functions on certain graded graphs: the Young lattice and its generalizations. Such functions first emerged in harmonic analysis on the infinite symmetric group. Our method relies on…
A numerical explicit method to evaluates transient solutions of linear partial differential non-homogeneous equation with constant coefficients is proposed.
Efficient computation of lattice defect geometries such as point defects, dislocations, disconnections, grain boundaries, interfaces and free surfaces requires accurate coupling of displacements near the defect to the long-range elastic…
This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…
We present a family of sense-preserving harmonic mappings in the unit disk related to the classical generalized (analytic) Koebe functions. We prove that these are precisely the mappings that maximize simultaneously the real part of every…