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 |
| Nashr sanasi | 2025-09-06 |
| Jild | 69 |
| Son | 3 |
| Betlar | 114-120 |
| DOI | 10.29229/uzmj.2025-3-11 |
DOI: 10.29229/uzmj.2025-3-11 · Maqolaning asl sahifasi
Total curvature, Monge-Ampere equation, ring domain, isotropic space, extrinsic curvature, boundary conditions.
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