Issue |
ESAIM: COCV
Volume 23, Number 4, October-December 2017
|
|
---|---|---|
Page(s) | 1381 - 1395 | |
DOI | https://doi.org/10.1051/cocv/2016058 | |
Published online | 06 September 2017 |
Optimizing the first eigenvalue of some quasilinear operators with respect to boundary conditions
1 Universitàdegli studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni R. Caccioppoli, Via Cintia, Monte S. Angelo – 80126 Napoli, Italia.
f.dellapietra@unina.it; nunzia.gavitone@unina.it
2 Università degli Studi di Brescia, DICATAM, Sezione di Matematica, Via Branze 38, 25123 Brescia, Italy.
hynek.kovarik@unibs.it
Received: 8 December 2015
Revised: 14 August 2016
Accepted: 31 August 2016
We consider a class of quasilinear operators on a bounded domain Ω ⊂ Rn 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.
Mathematics Subject Classification: 35P15sep 35P30 / 35J60
Key words: Robin boundary conditions / optimization problem / p −Laplacian
© EDP Sciences, SMAI 2017
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