Extremal problems dual to the Gauss variational problem

• Date: 2006
• Main Authors: Zorii, N. V., Зорий, Н. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2006
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3493
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We formulate and solve extremal problems of potential theory that are dual to the Gauss variational problem but, unlike the latter, are always solvable. Statements on the compactness of classes of solutions and the continuity of extremals are also established.