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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Volume 22, Number 1, Pages 140–152 (Mi timm1267)  
This article is cited in 4 scientific papers (total in 4 papers)

On the convergence of solutions of variational problems with bilateral obstacles in variable domains

A. A. Kovalevskyab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
Full-text PDF (197 kB) Citations (4)
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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.
Keywords: integral functional, minimizer, minimum value, bilateral obstacles, $\Gamma$-convergence, strong connected-ness.
Funding agency Grant number
Ural Branch of the Russian Academy of Sciences
Ministry of Education and Science of the Russian Federation 02.А03.21.0006
Received: 25.10.2015
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2017, Volume 296, Issue 1, Pages 151–163
DOI: https://doi.org/10.1134/S0081543817020146
Bibliographic databases:
Document Type: Article
UDC: 517.972
Language: Russian
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
Citation in format AMSBIB
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\pages 140--152
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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