O‘zbekiston matematika jurnali Volume 69 Issue 3 (2025) · pp. 114-120
Solution of the Monge-Ampere equation in a ring domain
Kholmurodova G.N.
Abstract
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.
Total curvature, Monge-Ampere equation, ring domain, isotropic space, extrinsic curvature, boundary conditions.
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