Contemporary Mathematics. Fundamental Directions
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Contemporary Mathematics. Fundamental Directions, 2010, Volume 35, Pages 33–43 (Mi cmfd143)  
On solutions with power-law singularities of the homogeneous Dirichlet problem for the Laplace equation in domains with biquadratic boundaries

V. P. Burskii, A. A. Telitsyna

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences, Ukraine, Donetsk
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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.
English version:
Journal of Mathematical Sciences, 2010, Volume 170, Issue 3, Pages 294–305
DOI: https://doi.org/10.1007/s10958-010-0086-8
Bibliographic databases:
Document Type: Article
UDC: 517.954
Language: Russian
Citation: V. P. Burskii, A. A. Telitsyna, “On solutions with power-law singularities of the homogeneous Dirichlet problem for the Laplace equation in domains with biquadratic boundaries”, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 1, CMFD, 35, PFUR, M., 2010, 33–43; Journal of Mathematical Sciences, 170:3 (2010), 294–305
Citation in format AMSBIB
\Bibitem{BurTel10}
\by V.~P.~Burskii, A.~A.~Telitsyna
\paper On solutions with power-law singularities of the homogeneous Dirichlet problem for the Laplace equation in domains with biquadratic boundaries
\inbook Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17--24, 2008). Part~1
\serial CMFD
\yr 2010
\vol 35
\pages 33--43
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd143}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2752637}
\transl
\jour Journal of Mathematical Sciences
\yr 2010
\vol 170
\issue 3
\pages 294--305
\crossref{https://doi.org/10.1007/s10958-010-0086-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77957738358}
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