We consider a class of quasilinear operators on a bounded domain and address the question of optimizing the first eigenvalue with respect to the boundary conditions, which are of the Robin-type. We describe the optimizing boundary conditions and establish upper and lower bounds on the respective maximal and minimal eigenvalue.
Mots clés : Robin boundary conditions, optimization problem, p −Laplacian
@article{COCV_2017__23_4_1381_0,
author = {Della Pietra, Francesco and Gavitone, Nunzia and Kova\v{r}{\'\i}k, Hynek},
title = {Optimizing the first eigenvalue of some quasilinear operators with respect to boundary conditions},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1381--1395},
publisher = {EDP-Sciences},
volume = {23},
number = {4},
year = {2017},
doi = {10.1051/cocv/2016058},
mrnumber = {3716925},
zbl = {1386.35294},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2016058/}
}
TY - JOUR AU - Della Pietra, Francesco AU - Gavitone, Nunzia AU - Kovařík, Hynek TI - Optimizing the first eigenvalue of some quasilinear operators with respect to boundary conditions JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1381 EP - 1395 VL - 23 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016058/ DO - 10.1051/cocv/2016058 LA - en ID - COCV_2017__23_4_1381_0 ER -
%0 Journal Article %A Della Pietra, Francesco %A Gavitone, Nunzia %A Kovařík, Hynek %T Optimizing the first eigenvalue of some quasilinear operators with respect to boundary conditions %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1381-1395 %V 23 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016058/ %R 10.1051/cocv/2016058 %G en %F COCV_2017__23_4_1381_0
Della Pietra, Francesco; Gavitone, Nunzia; Kovařík, Hynek. Optimizing the first eigenvalue of some quasilinear operators with respect to boundary conditions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1381-1395. doi : 10.1051/cocv/2016058. http://archive.numdam.org/articles/10.1051/cocv/2016058/
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