On one class of integral functionals with a variable domain of integration

1Shevchenko, AI
1Minenko, AS
1Donetsk National Technical University
Dopov. Nac. akad. nauk Ukr. 2014, 1:43-46
Section: Information Science and Cybernetics
Language: Russian

The potential-rotational current with free boundary is investigated. This variational task is equivalent to the problem of the minimum of an integral functional with a variable domain. The existence of the classical solution of a nonlinear boundary-value problem is proved.

Keywords: domain of integration, free boundary, integral functionals

1. Minenko A. S. Nelineinye granichnye zadachi, 1991, Iss. 3: 60–66 (in Russian).
2. Minenko A. S. Nelineinye granichnye zadachi, 1992, Iss. 4: 58-64 (in Russian).
3. Friedrichs K. O. Math. Ann., 1993, 109, No. 1: 60–82. https://doi.org/10.1007/BF01449125
4. Minenko A. S., Shevchenko A. I. Methods for investigating nonlinear mathematical models. Kyiv: Izd. IPII NAN Ukr., 2012 (in Russian).