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Asymptotic Expansions at Nonsymmetric Cuspidal Points

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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.

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Authors and Affiliations

  1. Institute of Mathematics, 14476, Potsdam, Germany

    I. Ly & N. Tarkhanov

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  1. I. Ly
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  2. N. Tarkhanov
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Correspondence to I. Ly.

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Ly, I., Tarkhanov, N. Asymptotic Expansions at Nonsymmetric Cuspidal Points. Math Notes 108, 219–228 (2020). https://doi.org/10.1134/S0001434620070238

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  • DOI: https://doi.org/10.1134/S0001434620070238

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