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On an explicit form of the Green function of the Robin problem for the Laplace operator in a circle
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Makhmud A. Sadybekov
,
Batirkhan K. Turmetov
Veröffentlicht/Copyright:
4. Juni 2015
Abstract
The paper is devoted to investigation questions about constructing the explicit form of the Green's function of the Robin problem in the unit ball of ℝ2. In constructing this function we use the representation of the fundamental solution of the Laplace equation in the form of a series. An integral representation of the Green function is obtained and for some values of the parameters the Green function is given in terms of elementary functions.
Keywords: Poisson equation; Robin problem; fundamental solution; Green's function; boundary value problems
Funding source: Ministry of Science and Education of the Republic of Kazakhstan
Award Identifier / Grant number: 0570/GF3
The authors would like to thank the editor and the referees for their valuable comments and remarks which led to a great improvement of the article.
Received: 2015-1-22
Revised: 2015-5-10
Accepted: 2015-5-11
Published Online: 2015-6-4
Published in Print: 2015-7-1
© 2015 by De Gruyter
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Artikel in diesem Heft
- Frontmatter
- Variations on a theorem of Beurling
- Dunkl harmonic analysis and fundamental sets of continuous functions on the unit sphere
- Boundary behavior of Green function for a parabolic equation in bounded domain
- On an explicit form of the Green function of the Robin problem for the Laplace operator in a circle
- Some properties of chain recurrent sets in a nonautonomous discrete dynamical system
- A joint generalization of Van Vleck's and Kannappan's equations on groups
Schlagwörter für diesen Artikel
Poisson equation;
Robin problem;
fundamental solution;
Green's function;
boundary value problems
Artikel in diesem Heft
- Frontmatter
- Variations on a theorem of Beurling
- Dunkl harmonic analysis and fundamental sets of continuous functions on the unit sphere
- Boundary behavior of Green function for a parabolic equation in bounded domain
- On an explicit form of the Green function of the Robin problem for the Laplace operator in a circle
- Some properties of chain recurrent sets in a nonautonomous discrete dynamical system
- A joint generalization of Van Vleck's and Kannappan's equations on groups
