Double-Layer Potentials for a Generalized Bi-Axially Symmetric Helmholtz Equation II

2018/07/08 by Berdyshev, Abdumauvlen, Hasanov, Anvar, Ergashev, Tuhtasin
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.03639

Abstract

The double-layer potential plays an important role in solving boundary value problems for elliptic equations. All the fundamental solutions of the generalized bi-axially symmetric Helmholtz 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 next fundamental solution. By using some properties of one of Appell's hypergeometric functions in two variables, we prove limiting theorems and derive integral equations concerning a denseness of double-layer potentials.

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