no. G10
Équations aux dérivées partielles, Physique mathématique
A Γ-convergence result for optimal design problems
Zorgati, Hamdi1, 2
1 Imam Mohammad Ibn Saud Islamic University (IMSIU), College of Science, Department of Mathematics and Statistics, PO-Box 90950, Riyadh 11623 Saudi Arabia
2 University of Tunis El Manar, Faculty of Sciences of Tunis, Department of Mathematics, Tunis 2092, Tunisia
Comptes Rendus. Mathématique, Tome 360 (2022) no. G10, pp. 1145-1151.

In this paper, we derive the Γ-limit of some optimal material distribution problems as the exponent goes to infinity.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.375
Classification : 74B20, 35E99, 35M10, 49J45
Zorgati, Hamdi 1, 2

1 Imam Mohammad Ibn Saud Islamic University (IMSIU), College of Science, Department of Mathematics and Statistics, PO-Box 90950, Riyadh 11623 Saudi Arabia
2 University of Tunis El Manar, Faculty of Sciences of Tunis, Department of Mathematics, Tunis 2092, Tunisia 
@article{CRMATH_2022__360_G10_1145_0,
     author = {Zorgati, Hamdi},
     title = {A $\Gamma $-convergence result for optimal design problems},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1145--1151},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     number = {G10},
     year = {2022},
     doi = {10.5802/crmath.375},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/crmath.375/}
}
TY  - JOUR
AU  - Zorgati, Hamdi
TI  - A $\Gamma $-convergence result for optimal design problems
JO  - Comptes Rendus. Mathématique
PY  - 2022
SP  - 1145
EP  - 1151
VL  - 360
IS  - G10
PB  - Académie des sciences, Paris
UR  - http://archive.numdam.org/articles/10.5802/crmath.375/
DO  - 10.5802/crmath.375
LA  - en
ID  - CRMATH_2022__360_G10_1145_0
ER  - 
%0 Journal Article
%A Zorgati, Hamdi
%T A $\Gamma $-convergence result for optimal design problems
%J Comptes Rendus. Mathématique
%D 2022
%P 1145-1151
%V 360
%N G10
%I Académie des sciences, Paris
%U http://archive.numdam.org/articles/10.5802/crmath.375/
%R 10.5802/crmath.375
%G en
%F CRMATH_2022__360_G10_1145_0
Zorgati, Hamdi. A $\Gamma $-convergence result for optimal design problems. Comptes Rendus. Mathématique, Tome 360 (2022) no. G10, pp. 1145-1151. doi : 10.5802/crmath.375. http://archive.numdam.org/articles/10.5802/crmath.375/

[1] Ansini, Nadia; Prinari, Francesca Power-law approximation under differential constraints, SIAM J. Math. Anal., Volume 46 (2014) no. 2, pp. 1085-1115 | DOI | MR | Zbl

[2] Ansini, Nadia; Prinari, Francesca On the lower semicontinuity of supremal functional under differential constraints, ESAIM, Control Optim. Calc. Var., Volume 21 (2015) no. 4, pp. 1053-1075 | DOI | MR | Zbl

[3] Barroso, Ana Cristina; Zappale, Elvira Relaxation for optimal design problems with non-standard growth, Appl. Math. Optim., Volume 80 (2019) no. 2, pp. 515-546 | DOI | MR | Zbl

[4] Bocea, Marian; Nesi, Vincenzo Γ-convergence of power-law functionals, variational principles in L ∞ , and applications, SIAM J. Math. Anal., Volume 39 (2008) no. 5, pp. 1550-1576 | DOI | MR | Zbl

[5] Braides, Andrea; Fonseca, Irene; Francfort, Gilles 3D-2D asymptotic analysis for inhomogeneous thin films, Indiana Univ. Math. J., Volume 49 (2000) no. 4, pp. 1367-1404 | MR | Zbl

[6] Carita, Graça; Zappale, Elvira 3D-2D dimensional reduction for a nonlinear optimal design problem with perimeter penalization, C. R. Math. Acad. Sci. Paris, Volume 350 (2012) no. 23-24, pp. 1011-1016 | DOI | MR | Zbl

[7] Champion, Thierry; De Pascale, Luigi; Prinari, Francesca Γ-convergence and absolute minimizers for supremal functionals, ESAIM: COCVC, Volume 10 (2004), pp. 14-27 | MR | Zbl

[8] Dal Maso, Gianni An Introduction to Γ-Convergence, Progress in Nonlinear Differential Equations and their Applications, 8, Birkhauser, Boston, 1993 | DOI

[9] De Giorgi, Ennio Sulla convergenza di alcune successioni di integrali del tipo dell area, Rend. Mat. (VI), Volume 8 (1975), pp. 277-294 | MR | Zbl

[10] Fonseca, Irene; Francfort, Gilles 3D-2D asymptotic analysis of an optimal design problem for thin films, J. Reine Angew. Math., Volume 505 (1998), pp. 173-202 | DOI | MR | Zbl

[11] Garroni, Adriana; Nesi, Vincenzo; Ponsiglione, Marcello Dielectric breakdown: Optimal bounds, Proc. R. Soc. Lond., Ser. A, Volume 457 (2001) no. 2014, pp. 2317-2335 | DOI | MR | Zbl

[12] Kozarzewski, Piotr A.; Zappale, Elvira A note on optimal design for thin structures in the Orlicz-Sobolev setting, Integral methods in science and engineering. Volume 1. Theoretical techniques, Birkhäuser; Springer, 2017, pp. 161-171 | DOI | Zbl

[13] Le Dret, Hervé; Raoult, Annie Variational Convergence for Nonlinear Shell Models with Directors and Related Semicontinuity and Relaxation Results, Arch. Ration. Mech. Anal., Volume 154 (2000) no. 2, pp. 101-134 | DOI | MR | Zbl

[14] Matias, José; Morandotti, Marco; Zappale, Elvira Optimal design of fractured media with prescribed macroscopic strain, J. Math. Anal. Appl., Volume 449 (2017) no. 2, pp. 1094-1132 | DOI | MR | Zbl

Cité par Sources :