In this paper we study the asymptotic behavior of some optimal design problems related to nonlinear Steklov eigenvalues, under irregular (but diffeomorphic) perturbations of the domain.
Accepté le :
DOI : 10.1051/cocv/2015050
Keywords: Shape optimization, Steklov eigenvalues, gamma convergence, oscillating domains
Bonder, Julián Fernández 1 ; Spedaletti, Juan F. 2
@article{COCV_2017__23_2_373_0,
author = {Bonder, Juli\'an Fern\'andez and Spedaletti, Juan F.},
title = {A shape optimization problem for {Steklov} eigenvalues in oscillating domains},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {373--390},
year = {2017},
publisher = {EDP Sciences},
volume = {23},
number = {2},
doi = {10.1051/cocv/2015050},
mrnumber = {3608085},
zbl = {1362.35198},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2015050/}
}
TY - JOUR AU - Bonder, Julián Fernández AU - Spedaletti, Juan F. TI - A shape optimization problem for Steklov eigenvalues in oscillating domains JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 373 EP - 390 VL - 23 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2015050/ DO - 10.1051/cocv/2015050 LA - en ID - COCV_2017__23_2_373_0 ER -
%0 Journal Article %A Bonder, Julián Fernández %A Spedaletti, Juan F. %T A shape optimization problem for Steklov eigenvalues in oscillating domains %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 373-390 %V 23 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2015050/ %R 10.1051/cocv/2015050 %G en %F COCV_2017__23_2_373_0
Bonder, Julián Fernández; Spedaletti, Juan F. A shape optimization problem for Steklov eigenvalues in oscillating domains. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 373-390. doi: 10.1051/cocv/2015050
A. Bensoussan, J.-L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structures. Corrected reprint of the 1978 original. AMS Chelsea Publishing, Providence, RI (2011). | Zbl | MR
A. Braides, -convergence for beginners, Vol. 22 of Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford (2002). | Zbl | MR
D. Cioranescu and F. Murat, A strange term coming from nowhere. In Topics in the Mathematical Modelling of Composite Materials. Vol. 31 of Progr. Nonlinear Differential Equations Appl. Birkhäuser Boston, Boston, MA (1997) 45–93. | Zbl | MR
G. Dal Maso, An introduction to -convergence. Vol. 8 of Progress in Nonlinear Differential Equations and their Applications. Birkhäuser Boston, Inc., Boston, MA (1993). | MR | Zbl
, and , Optimal boundary holes for the Sobolev trace constant. J. Differ. Eq. 251 (2011) 2327–2351. | Zbl | MR | DOI
, Windows of given area with minimal heat diffusion. Trans. Amer. Math. Soc. 351 (1999) 569–580. | Zbl | MR | DOI
, and , Optimization of the first Steklov eigenvalue in domains with holes: a shape derivative approach. Ann. Mat. Pura Appl. 186 (2007) 341–358. | Zbl | MR | DOI
, and , The best Sobolev trace constant in a domain with oscillating boundary. Nonlinear Anal. 67 (2007) 1173–1180. | Zbl | MR | DOI
and , Existence results for the -Laplacian with nonlinear boundary conditions. J. Math. Anal. Appl. 263 (2001) 195–223. | Zbl | MR | DOI
A. Henrot and M. Pierre, Variation et optimisation de formes. Une analyse géométrique (A geometric analysis). Vol. 48 of Mathématiques & Applications (Berlin) [Mathematics & Applications]. Springer, Berlin (2005). | Zbl | MR
E. Sánchez-Palencia, Nonhomogeneous media and vibration theory. Vol. 12 of Lect. Notes Phys. Springer-Verlag, Berlin, New York (1980). | Zbl | MR
J. Simon, Régularité de la solution d’une équation non linéaire dans . Journées d’Analyse Non Linéaire (Proc. Conf., Besançon, 1977). Vol. 665 of Lect. Notes Math. Springer, Berlin (1978) 205–227. | Zbl | MR
Cité par Sources :





