On étudie la Γ-convergence de fonctionelles non linéaires considérées dans des structures non périodiques de type de grille dans l'espace . La fonctionelle Γ-limite est obtenue sous forme explicite.
We study the Γ-convergence of nonlinear functionals considered in nonperiodic 2D lattice-like structures. The Γ-limit functional is obtained in the explicit form.
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@article{CRMATH_2002__335_3_315_0, author = {Pankratov, Leonid}, title = {\protect\emph{\ensuremath{\Gamma}}-convergence of nonlinear functionals in thin reticulated structures}, journal = {Comptes Rendus. Math\'ematique}, pages = {315--320}, publisher = {Elsevier}, volume = {335}, number = {3}, year = {2002}, doi = {10.1016/S1631-073X(02)02468-8}, language = {en}, url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02468-8/} }
TY - JOUR AU - Pankratov, Leonid TI - Γ-convergence of nonlinear functionals in thin reticulated structures JO - Comptes Rendus. Mathématique PY - 2002 SP - 315 EP - 320 VL - 335 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02468-8/ DO - 10.1016/S1631-073X(02)02468-8 LA - en ID - CRMATH_2002__335_3_315_0 ER -
%0 Journal Article %A Pankratov, Leonid %T Γ-convergence of nonlinear functionals in thin reticulated structures %J Comptes Rendus. Mathématique %D 2002 %P 315-320 %V 335 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02468-8/ %R 10.1016/S1631-073X(02)02468-8 %G en %F CRMATH_2002__335_3_315_0
Pankratov, Leonid. Γ-convergence of nonlinear functionals in thin reticulated structures. Comptes Rendus. Mathématique, Tome 335 (2002) no. 3, pp. 315-320. doi : 10.1016/S1631-073X(02)02468-8. http://www.numdam.org/articles/10.1016/S1631-073X(02)02468-8/
[1] Homogenization: Averaging Processes in Periodic Media, Kluwer Academic, Dordrecht, 1989
[2] Asymptotic Analysis for Periodic Structures, Stud. Math. Appl., 5, North-Holland, Amsterdam, 1978
[3] Homogenization of Multiple Integrals, Oxford Lecture Ser. Math. Appl., 12, Clarendon Press, Oxford, 1998
[4] Homogenization of Reticulated Structures, Appl. Math. Sci., 136, Springer-Verlag, New York, 1999
[5] D. Cioranescu, M.V. Goncharenko, F. Murat, L.S. Pankratov, Homogenization of nonlinear variational problems in domains of degenerating measure, prepared for publication
[6] An Introduction to Γ-Convergence, Birkhäuser, Boston, 1993
[7] Homogenization of the Dirichlet variational problems in Orlicz–Sobolev spaces, Oper. Theory Appl., Fields Inst. Commun., 25, American Mathematical Society, Providence, RI, 2000, pp. 345-366
[8] Conditions of the Γ-convergence and homogenization of integral functionals with different domains of the definition, Dokl. Akad. Nauk Ukrainy, Volume 4 (1991), pp. 5-8 (in Russian)
[9] Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1973
[10] L.S. Pankratov, On convergence of the solutions of variational problems in weakly connected domains, Preprint 53-88, Institute for Low Temperature Physics and Engineering, Kharkov, 1988 (in Russian)
[11] Nonhomogeneous Media and Vibration Theory, Lecture Notes in Phys., 127, Springer-Verlag, New York, 1980
[12] Asymptotic behavior of the solutions of the second boundary value problem in domains of decreasing volume, Operator Theory and Subharmonic Functions, Naukova Dumka, Kiev, 1991, pp. 126-134 (in Russian)
[13] Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, New York, 1994
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