Geodesic
On the Convergence of Solutions of Variational Problems with Implicit Pointwise Constraints in Variable Domains
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 2, pp. 82-85

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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
Mots-clés : $\Gamma$-convergence, variable domain. 
@article{FAA_2018_52_2_a7,
     author = {A. A. Kovalevsky},
     title = {On the {Convergence} of {Solutions} of {Variational} {Problems} with {Implicit} {Pointwise} {Constraints} in {Variable} {Domains}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {82--85},
     publisher = {mathdoc},
     volume = {52},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2018_52_2_a7/}
}
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A. A. Kovalevsky. On the Convergence of Solutions of Variational Problems with Implicit Pointwise Constraints in Variable Domains. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 2, pp. 82-85. http://geodesic.mathdoc.fr/item/FAA_2018_52_2_a7/