At present the fundamental solutions of the multidimensional singular elliptic equation are known and they are expressed through the well-known Lauricella function $F_A^{(n)}$, the number of variables of which is equal to the number of singular coefficients of the equation under consideration. On the other hand, in applications of any hypergeometric function of many variables, expansion formulas are very important, allowing one to represent this hypergeometric function as an infinite sum of products of one-dimensional hypergeometric Gaussian functions for each variable of the studied function of many variables. In this paper we study one mixed problem for an elliptic equation with many singular coefficients in the first hyperoctant of the unit ball, the uniqueness of its solution is proved by the method of energy integrals, and its existence by the Green's function method. When finding the desired solution, expansion and summation formulas are used, as well as the limit relation for the Lauricella function.
| Mualliflar | Hasanov, A., Ergashev, T., Tulakova, Z. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2026-07-02 |
| Jild | 70 |
| Son | 2 |
| Betlar | 74-82 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2026-2-9 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2026-2-9 · Maqolaning asl sahifasi
multidimensional elliptic equations with singular coefficients, fundamental solution, Gauss hypergeometric function, Lauricella function, mixed problem, Green's function
| APA | Hasanov, A., Ergashev, T., & Tulakova, Z. (2026). On a mixed problem for a multidimensional elliptic equation with singular coefficients. O‘zbekiston matematika jurnali, 70(2), 74-82. https://doi.org/10.29229/uzmj.2026-2-9 |
|---|---|
| GOST (OAK) | Hasanov, A., Ergashev, T., Tulakova, Z. On a mixed problem for a multidimensional elliptic equation with singular coefficients // O‘zbekiston matematika jurnali. – 2026. – T. 70, № 2. – P. 74-82. – DOI: 10.29229/uzmj.2026-2-9. |
| MLA | Hasanov, A., Ergashev, T., and Tulakova, Z. “On a mixed problem for a multidimensional elliptic equation with singular coefficients.” O‘zbekiston matematika jurnali, 70(2), 74-82, 2026. https://doi.org/10.29229/uzmj.2026-2-9 |
| Chicago | Hasanov, A., Ergashev, T., and Tulakova, Z. “On a mixed problem for a multidimensional elliptic equation with singular coefficients.” O‘zbekiston matematika jurnali, 70(2), 74-82 (2026). https://doi.org/10.29229/uzmj.2026-2-9 |
| Harvard | Hasanov, A., Ergashev, T., and Tulakova, Z (2026) ‘On a mixed problem for a multidimensional elliptic equation with singular coefficients’, O‘zbekiston matematika jurnali, 70(2), 74-82. https://doi.org/10.29229/uzmj.2026-2-9 |
| BibTeX | @article{hasanova2026,
title = {On a mixed problem for a multidimensional elliptic equation with singular coefficients},
author = {Hasanov, A. and Ergashev, T. and Tulakova, Z.},
journal = {O‘zbekiston matematika jurnali},
year = {2026},
volume = {70},
number = {2},
pages = {74-82},
doi = {10.29229/uzmj.2026-2-9},
url = {https://doi.org/10.29229/uzmj.2026-2-9}
} |
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