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Mathematics > Analysis of PDEs

arXiv:1807.00903 (math)
[Submitted on 2 Jul 2018]

Title:Third Double-layer Potential for generalized bi-axially symmetric Helmholtz equation

Authors:Tuhtasin Ergashev
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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 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.
Comments: 13 pages, in Russian
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1807.00903 [math.AP]
  (or arXiv:1807.00903v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1807.00903

Submission history

From: Tuhtasin Ergashev [view email]
[v1] Mon, 2 Jul 2018 21:42:39 UTC (13 KB)
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