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On the Dirichlet Problem with Corner Singularity

Author

Listed:
  • Viktor A. Rukavishnikov

    (Computing Center of Far-Eastern Branch, Russian Academy of Sciences, Kim-Yu-Chen Str. 65, 680000 Khabarovsk, Russia)

  • Elena I. Rukavishnikova

    (Computing Center of Far-Eastern Branch, Russian Academy of Sciences, Kim-Yu-Chen Str. 65, 680000 Khabarovsk, Russia)

Abstract

We consider the Dirichlet problem for an elliptic equation with a singularity. The singularity of the solution to the problem is caused by the presence of a re-entrant corner at the boundary of the domain. We define an R ν -generalized solution for this problem. This allows for the construction of numerical methods for finding an approximate solution without loss of accuracy. In this paper, the existence and uniqueness of the R ν -generalized solution in set W ∘ 2 , α 1 ( Ω , δ ) is proven. The R ν -generalized solution is the same for different parameters ν .

Suggested Citation

  • Viktor A. Rukavishnikov & Elena I. Rukavishnikova, 2020. "On the Dirichlet Problem with Corner Singularity," Mathematics, MDPI, vol. 8(11), pages 1-7, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1870-:d:436466
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    Cited by:

    1. Viktor A. Rukavishnikov & Alexey V. Rukavishnikov, 2022. "On the Properties of Operators of the Stokes Problem with Corner Singularity in Nonsymmetric Variational Formulation," Mathematics, MDPI, vol. 10(6), pages 1-32, March.

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