Geodesic
Optimizing the first eigenvalue of some quasilinear operators with respect to boundary conditions
Della Pietra, Francesco1 ; Gavitone, Nunzia1 ; Kovařík, Hynek2
1 Universitàdegli studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni R. Caccioppoli, Via Cintia, Monte S. Angelo – 80126 Napoli, Italia.
2 Università degli Studi di Brescia, DICATAM, Sezione di Matematica, Via Branze 38, 25123 Brescia, Italy.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1381-1395 Cet article a éte moissonné depuis la source Numdam

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We consider a class of quasilinear operators on a bounded domain Ω⊂R n 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.

DOI : 10.1051/cocv/2016058
Classification : 35P15sep 35P30, 35J60
Keywords: Robin boundary conditions, optimization problem, p −Laplacian

Della Pietra, Francesco 1 ; Gavitone, Nunzia 1 ; Kovařík, Hynek 2

1 Universitàdegli studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni R. Caccioppoli, Via Cintia, Monte S. Angelo – 80126 Napoli, Italia.
2 Università degli Studi di Brescia, DICATAM, Sezione di Matematica, Via Branze 38, 25123 Brescia, Italy. 
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     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},
     year = {2017},
     publisher = {EDP-Sciences},
     volume = {23},
     number = {4},
     doi = {10.1051/cocv/2016058},
     mrnumber = {3716925},
     zbl = {1386.35294},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016058/}
}
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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

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