The problem of recovering surfaces by the total or extrinsic curvature is related to the solution of the nonlinear elliptic equation of the Monge-Ampere type. Using the geometric method, the existence and uniqueness of a solution to the Monge-Ampere equation is shown in the problem of recovering a surface by its total curvature in isotropic space. In this article, an exact solution to the Dirichlet problem for a ring domain is found if the total curvature function is given exact form. In this, isotropic space geometry is used.
| Mualliflar | Kholmurodova G.N. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2025-09-06 |
| Jild | 69 |
| Son | 3 |
| Betlar | 114-120 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2025-3-11 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2025-3-11 · Maqolaning asl sahifasi
Total curvature, Monge-Ampere equation, ring domain, isotropic space, extrinsic curvature, boundary conditions.
| APA | Kholmurodova G.N. (2025). Solution of the Monge-Ampere equation in a ring domain. O‘zbekiston matematika jurnali, 69(3), 114-120. https://doi.org/10.29229/uzmj.2025-3-11 |
|---|---|
| GOST (OAK) | Kholmurodova G.N. Solution of the Monge-Ampere equation in a ring domain // O‘zbekiston matematika jurnali. – 2025. – T. 69, № 3. – P. 114-120. – DOI: 10.29229/uzmj.2025-3-11. |
| MLA | Kholmurodova G.N. “Solution of the Monge-Ampere equation in a ring domain.” O‘zbekiston matematika jurnali, 69(3), 114-120, 2025. https://doi.org/10.29229/uzmj.2025-3-11 |
| Chicago | Kholmurodova G.N. “Solution of the Monge-Ampere equation in a ring domain.” O‘zbekiston matematika jurnali, 69(3), 114-120 (2025). https://doi.org/10.29229/uzmj.2025-3-11 |
| Harvard | Kholmurodova G.N (2025) ‘Solution of the Monge-Ampere equation in a ring domain’, O‘zbekiston matematika jurnali, 69(3), 114-120. https://doi.org/10.29229/uzmj.2025-3-11 |
| BibTeX | @article{kholmurodovagn2025,
title = {Solution of the Monge-Ampere equation in a ring domain},
author = {Kholmurodova G.N.},
journal = {O‘zbekiston matematika jurnali},
year = {2025},
volume = {69},
number = {3},
pages = {114-120},
doi = {10.29229/uzmj.2025-3-11},
url = {https://doi.org/10.29229/uzmj.2025-3-11}
} |
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