Abstract:
We establish sufficient conditions for the convergence of minimizers and minimum values of integral and more general functionals on sets of functions defined by bilateral obstacles in variable domains. The given obstacles are elements of the corresponding Sobolev space, and the degeneration on a set of measure zero is admitted for the difference of the upper and lower obstacles. We show that a weakening of the condition of positivity of this difference on a set of full measure may lead to a certain violation of the established convergence result.
Citation:
A. A. Kovalevsky, “On the convergence of solutions of variational problems with bilateral obstacles in variable domains”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 1, 2016, 140–152; Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 151–163
\Bibitem{Kov16}
\by A.~A.~Kovalevsky
\paper On the convergence of solutions of variational problems with bilateral obstacles in variable domains
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 1
\pages 140--152
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2017
\vol 296
\issue , suppl. 1
\pages 151--163
\crossref{https://doi.org/10.1134/S0081543817020146}
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Linking options:
https://www.mathnet.ru/eng/timm1267
https://www.mathnet.ru/eng/timm/v22/i1/p140
This publication is cited in the following 4 articles:
Alexander A. Kovalevsky, “Convergence of solutions of variational problems with measurable bilateral constraints in variable domains”, Annali di Matematica, 201:2 (2022), 835
A. A. Kovalevsky, “Variational problems with variable regular bilateral constraints in variable domains”, Rev. Mat. Complut., 32:2 (2019), 327–351
A. A. Kovalevsky, “On the convergence of solutions of variational problems with variable implicit pointwise constraints in variable domains”, Ann. Mat. Pura Appl., 198:4 (2019), 1087–1119
A. A. Kovalevsky, “On the Convergence of Solutions of Variational Problems with Implicit Pointwise Constraints in Variable Domains”, Funct. Anal. Appl., 52:2 (2018), 147–150
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