A. A. Kovalevsky, “On the Convergence of Solutions of Variational Problems with Implicit Pointwise Constraints in Variable Domains”, Funktsional. Anal. i Prilozhen., 2018, Volume 52, Issue 2,Pages <nobr>82

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Brief communications

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

A. A. Kovalevsky^ab

^a Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia
^b Ural Federal University, Yekaterinburg, Russia

Abstract: Results on the convergence of minimizers and minimum values of integral and more general functionals $J_s\colon W^{1,p}(\Omega_s)\to\mathbb R$ on the sets $U_s(h_s)=\{v\in W^{1,p}(\Omega_s)\colon h_s(v)\leqslant 0\ \text{a.e.\ in }\Omega_s\}$, where $p>1$, $\{\Omega_s\}$ is a sequence of domains contained in a bounded domain $\Omega$ of $\mathbb R^n$ ($n\geqslant 2$), and $\{h_s\}$ is a sequence of functions on $\mathbb R$, are announced.

Keywords: integral functional, variational problem, implicit pointwise constraint, minimizer, minimum value, $\Gamma$-convergence, variable domain.

UDC: 517.972

Received: 29.05.2017

DOI: 10.4213/faa3496