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On solutions with power-law singularities of the homogeneous Dirichlet problem for the Laplace equation in domains with biquadratic boundaries

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Abstract

Properties of the Dirichlet problem for the Laplace equation in a bounded plane domain of a special type are studied in a certain class of solutions with power-law singularities. We prove that if a harmonic function is allowed to have a finite number of poles, then it can satisfy the trivial Dirichlet condition on certain curves of the studied family. The specified curves are selected, and it is shown that the set of those curves is dense (in a certain sense) in the studied family.

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Authors and Affiliations

  1. Institute of Applied Mathematics NASU, Donetsk, Ukraine

    V. P. Burskii & A. A. Telitsyna

Authors
  1. V. P. Burskii
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  2. A. A. Telitsyna
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Correspondence to V. P. Burskii.

Additional information

Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 35, Proceedings of the Fifth International Conference on Differential and Functional Differential Equations. Part 1, 2010.

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Burskii, V.P., Telitsyna, A.A. On solutions with power-law singularities of the homogeneous Dirichlet problem for the Laplace equation in domains with biquadratic boundaries. J Math Sci 170, 294–305 (2010). https://doi.org/10.1007/s10958-010-0086-8

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  • DOI: https://doi.org/10.1007/s10958-010-0086-8

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