On Boundary Values of Three-Harmonic Poisson Integral on the Boundary of a Unit Disk

2018 ◽  
Vol 70 (7) ◽  
pp. 1012-1021 ◽  
Author(s):  
S. B. Hembars’ka
Keyword(s):  
Unit Disk ◽  
Poisson Integral ◽  
Boundary Values

scholarly journals A test for Picard principle

1975 ◽  
Vol 56 ◽  
pp. 105-119 ◽  
Author(s):  
Mitsuru Nakai
Keyword(s):  
Continuous Function ◽  
Unit Disk ◽  
Boundary Values ◽  
Hölder Continuous ◽  
Nonnegative Solutions

A nonnegative locally Hölder continuous function P(z) on 0 < | z | ≤ 1 will be referred to as a density on 0 < | z | ≤ 1. The elliptic dimension of a density P(z) at z = 0, dim P in notation, is defined to be the dimension of the half module of nonnegative solutions of the equation Δu(z) = P(z)u(z) on the punctured unit disk Ω : 0 < | z | < 1 with boundary values zero on | z | = 1. After Bouligand we say that the Picard principle is valid for a density P at z = 0 if dim P = 1.

Green's Potentials with Prescribed Boundary Values

1977 ◽  
Vol 29 (4) ◽  
pp. 681-686
Author(s):  
Jang-Mei G. Wu
Keyword(s):  
Green’S Function ◽  
Unit Disk ◽  
Mass Distribution ◽  
Green's Function ◽  
Open Unit ◽  
Open Unit Disk ◽  
Boundary Values ◽  
Image Position

Let U, C denote the open unit disk and unit circumference, respectively and G(z, w) be the Green's function on U. We say v is the Green's potential of a mass distribution v on U if

Corrigenda: Cauchy and Poisson integral representations for ultradistributions of compact support and distributional boundary values

1984 ◽  
Vol 96 (1-2) ◽  
pp. 179-179 ◽  
Author(s):  
R. S. Pathak
Keyword(s):  
Compact Support ◽  
Integral Representations ◽  
Poisson Integral ◽  
Boundary Values

Page 56: In the estimate , C1 = CSn/(2πσ)n, h = (2πσ)−1 where σ depends on y. Therefore, {fy(t)} may not be bounded in as y → 0, y ∈ C′.

A Radial Derivative with Boundary Values of the Spherical Poisson Integral

1999 ◽  
Vol 6 (1) ◽  
pp. 19-32
Author(s):  
O. Dzagnidze
Keyword(s):  
Poisson Integral ◽  
Boundary Values ◽  
Cartesian Coordinates ◽  
Radial Derivative ◽  
Partial Derivatives ◽  
Spherical Poisson Integral

Abstract A formula of a radial derivative is obtained with the aid of derivatives with respect to θ and to φ of the functions closely connected with the spherical Poisson integral 𝑢f (r, θ, φ) and the boundary values are determined for . The boundary values are also found for partial derivatives with respect to the Cartesian coordinates , and .

The Yukawa Potential Function and Reciprocal Univalent Function

2013 ◽  
Vol 3 (2) ◽  
pp. 197-202
Author(s):  
Amir Pishkoo ◽  
Maslina Darus
Keyword(s):  
Mathematical Model ◽  
Unit Disk ◽  
Potential Function ◽  
Univalent Function ◽  
Open Problem ◽  
Yukawa Potential ◽  
Reciprocal Theorem ◽  
Problem Statement ◽  
Fundamental Forces

This paper presents a mathematical model that provides analytic connection between four fundamental forces (interactions), by using modified reciprocal theorem,derived in the paper, as a convenient template. The essential premise of this work is to demonstrate that if we obtain with a form of the Yukawa potential function [as a meromorphic univalent function], we may eventually obtain the Coloumb Potential as a univalent function outside of the unit disk. Finally, we introduce the new problem statement about assigning Meijer's G-functions to Yukawa and Coloumb potentials as an open problem.

On a Subclass of Univalent Harmonic Mappings Convex in the Imaginary Direction

2020 ◽  
pp. 445-454
Author(s):  
Deepali Khurana ◽  
Sushma Gupta ◽  
Sukhjit Singh
Keyword(s):  
Present Article ◽  
Unit Disk ◽  
Imaginary Axis ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Distortion Bounds ◽  
Univalent Harmonic Mappings

In the present article, we consider a class of univalent harmonic mappings, $\mathcal{C}_{T} = \left\{ T_{c}[f] =\frac{f+czf'}{1+c}+\overline{\frac{f-czf'}{1+c}}; \; c>0\;\right\}$ and $f$ is convex univalent in $\mathbb{D}$, whose functions map the open unit disk $\mathbb{D}$ onto a domain convex in the direction of the imaginary axis. We estimate coefficient, growth and distortion bounds for the functions of the same class.

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