Abstract
Results on the convergence of minimizers and minimum values of integral and more general functionals Js: W1,p(Ωs) → ℝ on the sets Us(hs) = {v ∈ W1,p(Ωs): hs(v) ≤ 0 a.e. in Ωs}, where p > 1, {Ωs} is a sequence of domains contained in a bounded domain Ω of ℝn (n > 2), and {hs} is a sequence of functions on ℝ, are announced.
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A. A. Kovalevskii, in: Current Analysis and its Applications [in Russian], Naukova Dumka, Kiev, 1989, 62–70.
A. A. Kovalevsky, Trudy Inst. Math. Mech. UrO Ross. Akad. Nauk, 22:1 (2016), 140-152; English transl.: Proc. Steklov Inst. Math., 296, Suppl. 1 (2017), 151–163.
E. Ya. Khruslov, Mat. Sb., 106(148):4(8) (1978), 604-621; English transl.: Math. USSR Sb., 35:2 (1979), 266–282.
A. A. Kovalevskii, Nelinein. Granichnye Zadachi, 4 (1992), 29–39.
V. V. Zhikov, Izv. Akad. Nauk SSSR, Ser. Math., 47:5 (1983), 961-998; English transl.: Math. USSR Izv., 23:2 (1984), 243–276.
G. Dal Maso, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Natur. (8), 74:2 (1983), 55–61.
G. Dal Maso, Ann. Mat. Pura Appl. (4), 129:1 (1981), 327–366.
M. M. Vainberg, Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations, Wiley, New York, 1973.
K. Kuratowski, Topology, vol. I, Academic Press, New York-London, 1966.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 52, No. 2, pp. 82{85, 2018
Original Russian Text Copyright © by A. A. Kovalevsky
This work was supported by the Russian Academic Excellence Project (agreement no. 02.A03.21.0006 of August 27, 2013, between the Ministry of Education and Science of the Russian Federation and Ural Federal University).
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Kovalevsky, A.A. On the Convergence of Solutions of Variational Problems with Implicit Pointwise Constraints in Variable Domains. Funct Anal Its Appl 52, 147–150 (2018). https://doi.org/10.1007/s10688-018-0221-8
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DOI: https://doi.org/10.1007/s10688-018-0221-8