2018/07/02 by Tuhtasin Ergashev, Ergashev, Tuhtasin
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1807.00903
openalex publication_date 2018/07/02 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28
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 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 third 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.