The Fourth Double-Layer Potential for a Generalized Bi-Axially Symmetric Helmholtz Equation

TL;DR

This paper develops the theory of double-layer potentials for the fourth fundamental solution of a generalized bi-axially symmetric Helmholtz equation, expanding the potential theory beyond the first fundamental solution.

Contribution

It introduces the construction of the double-layer potential theory for the fourth fundamental solution of the generalized bi-axially symmetric Helmholtz equation, previously only developed for the first solution.

Findings

Established the theory for the fourth fundamental solution

Extended potential theory to new fundamental solutions

Provided mathematical framework for boundary value problems

Abstract

The double-layer potential plays an important role in solving boundary value problems for elliptic equations, and in the study of which for a certain equation, the properties of the fundamental solutions of the given equation are used. All the fundamental solutions of the generalized bi-axially symmetric Helmholts equation were known, and only for the first one was constructed the theory of potential. Here, in this paper, we aim at constructing theory of double-layer potentials corresponding to the fourth fundamental solution.