The Dirichlet problem for elliptic equation with several singular coefficients
Recently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the Dirichlet problem for an elliptic equation with several singula...
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| Format: | Article |
| Language: | English |
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EJAAM
2019-07-01
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| Series: | E-Journal of Analysis and Applied Mathematics |
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| Online Access: | https://ejaam.org/articles/2018/10.2478-ejaam-2018-0006.pdf |
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| author | Tuhtasin G. Ergashev |
| author_facet | Tuhtasin G. Ergashev |
| author_sort | Tuhtasin G. Ergashev |
| collection | DOAJ |
| description | Recently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the Dirichlet problem for an elliptic equation with several singular coefficients in explicit form. When finding a solution, we use decomposition formulas and some adjacent relations for the Lauricella hypergeometric function in many variables. |
| format | Article |
| id | doaj-art-4f62884710a54060a600583061bac720 |
| institution | Kabale University |
| issn | 2544-9990 |
| language | English |
| publishDate | 2019-07-01 |
| publisher | EJAAM |
| record_format | Article |
| series | E-Journal of Analysis and Applied Mathematics |
| spelling | doaj-art-4f62884710a54060a600583061bac7202025-02-08T18:35:22ZengEJAAME-Journal of Analysis and Applied Mathematics2544-99902019-07-01201810.2478/ejaam-2018-0006The Dirichlet problem for elliptic equation with several singular coefficientsTuhtasin G. Ergashev0V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 100170, Tashkent, UzbekistanRecently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the Dirichlet problem for an elliptic equation with several singular coefficients in explicit form. When finding a solution, we use decomposition formulas and some adjacent relations for the Lauricella hypergeometric function in many variables.https://ejaam.org/articles/2018/10.2478-ejaam-2018-0006.pdfdirichlet problemmultidimensional elliptic equationssingular coefficientsdecomposition formulaslauricella hypergeometric function |
| spellingShingle | Tuhtasin G. Ergashev The Dirichlet problem for elliptic equation with several singular coefficients E-Journal of Analysis and Applied Mathematics dirichlet problem multidimensional elliptic equations singular coefficients decomposition formulas lauricella hypergeometric function |
| title | The Dirichlet problem for elliptic equation with several singular coefficients |
| title_full | The Dirichlet problem for elliptic equation with several singular coefficients |
| title_fullStr | The Dirichlet problem for elliptic equation with several singular coefficients |
| title_full_unstemmed | The Dirichlet problem for elliptic equation with several singular coefficients |
| title_short | The Dirichlet problem for elliptic equation with several singular coefficients |
| title_sort | dirichlet problem for elliptic equation with several singular coefficients |
| topic | dirichlet problem multidimensional elliptic equations singular coefficients decomposition formulas lauricella hypergeometric function |
| url | https://ejaam.org/articles/2018/10.2478-ejaam-2018-0006.pdf |
| work_keys_str_mv | AT tuhtasingergashev thedirichletproblemforellipticequationwithseveralsingularcoefficients AT tuhtasingergashev dirichletproblemforellipticequationwithseveralsingularcoefficients |