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Matematicheskie Zametki, 2020, Volume 108, Issue 2, paper published in the English version journal
(Mi mzm12591)
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Papers published in the English version of the journal
Asymptotic Expansions at Nonsymmetric Cuspidal Points
I. Ly, N. Tarkhanov Institute of Mathematics, Potsdam, 14476 Germany
Abstract:
We study the asymptotics of solutions to the Dirichlet problem in a domain
$\mathcal{X}
\subset \mathbb{R}^3$
whose
boundary contains a singular point
$O$.
In a small neighborhood of this point, the domain has the form
$\{ z > \sqrt{x^2 + y^4}
\}$,
i.e., the origin is a nonsymmetric conical point at the boundary.
So far, the behavior of solutions to elliptic boundary-value problems has not been studied sufficiently
in the case of nonsymmetric singular points.
This problem was posed by V.A. Kondrat'ev in 2000.
We establish a complete asymptotic expansion of solutions near the singular point.
Keywords:
Dirichlet problem, singular points, asymptotic expansions.
Received: 20.10.2019
Citation:
I. Ly, N. Tarkhanov, “Asymptotic Expansions at Nonsymmetric Cuspidal Points”, Math. Notes, 108:2 (2020), 219–228
Linking options:
https://www.mathnet.ru/eng/mzm12591
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Abstract page: | 74 |
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