On the Convergence of Solutions of Variational Problems with Implicit Pointwise Constraints in Variable Domains


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Results on the convergence of minimizers and minimum values of integral and more general functionals Js: W1,ps) → ℝ on the sets Us(hs) = {vW1,ps): 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. Kovalevsky

Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences; Ural Federal University

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