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

Authors

  • A.I. Shevchenko
  • A.S. Minenko

DOI:

https://doi.org/10.15407/dopovidi2014.01.043

Keywords:

domain of integration, free boundary, integral functionals

Abstract

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.

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References

Minenko A. S. Nelineinye granichnye zadachi, 1991, Iss. 3: 60–66 (in Russian).

Minenko A. S. Nelineinye granichnye zadachi, 1992, Iss. 4: 58-64 (in Russian).

Friedrichs K. O. Math. Ann., 1993, 109, No. 1: 60–82. https://doi.org/10.1007/BF01449125

Minenko A. S., Shevchenko A. I. Methods for investigating nonlinear mathematical models. Kyiv: Izd. IPII NAN Ukr., 2012 (in Russian).

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Published

24.03.2025

How to Cite

Shevchenko, A., & Minenko, A. (2025). On one class of integral functionals with a variable domain of integration . Reports of the National Academy of Sciences of Ukraine, (1), 43–46. https://doi.org/10.15407/dopovidi2014.01.043

Issue

No. 1 (2014): Reports of the National Academy of Sciences of Ukraine

Section

Information Science and Cybernetics

License

Copyright (c) 2025 Reports of the National Academy of Sciences of Ukraine

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