Double-layer potentials for a generalized bi-axially symmetric Helmholtz equation. II. (English) Zbl 1433.35014
Summary: In earlier papers, the double-layer potential has been successfully applied in solving boundary value problems for elliptic equations. All the fundamental solutions of the generalized bi-axially symmetric Helmholtz equation were known [the second author, Complex Var. Elliptic Equ. 52, No. 8, 673–683 (2007; Zbl 1147.35018)], while the potential theory was constructed only for the first one [H. M. Srivastava, the second author and J. Choi, “Double-layer potentials for a generalized bi-axially symmetric
Helmholtz equation”, Sohag J Math. 2(1), 1–10 (2015)]. Here, in this paper, our goal is to construct theory of double-layer potentials corresponding to the next fundamental solution. We used some properties of one of Appell’s hypergeometric functions with respect to two variables to prove the limiting theorems, while integral equations concerning the denseness of double-layer potentials are derived.
MSC:
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
Citations:
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