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Variational problems with variable regular bilateral constraints in variable domains

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Abstract

We establish conditions for the convergence of minimizers and minimum values of integral and more general functionals on sets of functions defined by bilateral constraints in variable domains. The constraints and domains under consideration depend on the same natural parameter, and the constraints belong to Sobolev spaces related to the given domains. The main condition on the constraints is the convergence to zero of the measure of the set where the difference between the upper and lower constraints is less than a positive measurable function.

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Acknowledgements

This work was partially 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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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Sofia Kovalevskaya St. 16, Yekaterinburg, Russia, 620990

    Alexander A. Kovalevsky

  2. Institute of Natural Sciences and Mathematics, Ural Federal University, pr. Lenina 51, Yekaterinburg, Russia, 620000

    Alexander A. Kovalevsky

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  1. Alexander A. Kovalevsky
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Correspondence to Alexander A. Kovalevsky.

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Kovalevsky, A.A. Variational problems with variable regular bilateral constraints in variable domains. Rev Mat Complut 32, 327–351 (2019). https://doi.org/10.1007/s13163-018-0281-6

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  • DOI: https://doi.org/10.1007/s13163-018-0281-6

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