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Solution of the Monge-Ampere equation in a ring domain
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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.
Title: Solution of the Monge-Ampere equation in a ring domain
Description:
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.
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