JOURNAL ARTICLE

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

  • Published In: Uzbek Mathematical Journal, 2025, v. 69, n. 3. P. 114 1 of 3

  • Database: Mathematics Source 2 of 3

  • Authored By: G. N., Kholmurodova 3 of 3

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. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Uzbek Mathematical Journal. 2025/07, Vol. 69, Issue 3, p114
  • Document Type:Article
  • Subject Area:History
  • Publication Date:2025
  • ISSN:2010-7269
  • DOI:10.29229/uzmj.2025-3-11
  • Accession Number:187771176
  • Copyright Statement:Copyright of Uzbek Mathematical Journal is the property of Uzbekistan Academy of Sciences, Institute of Mathematics named after V.I. Romanovskiy and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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