On minimization of one integral functional by the Ritz method

• Date: 2006
• Main Authors: Minenko, A. S., Миненко, А. С.
• 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/3540
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Using the variational method, we investigate a nonlinear problem with a Bernoulli condition in the form of an inequality on a free boundary. We prove a solvability theorem and establish the convergence of an approximate solution obtained by the Ritz method to the exact solution in certain metrics.