Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 8 (2009) no. 1, pp. 51-71.

The first eigenvalue of the p-Laplacian on an open set of given measure attains its minimum value if and only if the set is a ball. We provide a quantitative version of this statement by an argument that can be easily adapted to treat also certain isocapacitary and Cheeger inequalities.

Classification: 49R50, 35J20, 49J40, 26D20
Fusco, Nicola 1; Maggi, Francesco 2; Pratelli, Aldo 3

1 Dipartimento di Matematica e Applicazioni, Via Cintia, 80126 Napoli, Italia
2 Dipartimento di Matematica, Viale Morgagni, 67/A, 50134 Firenze, Italia
3 Dipartimento di Matematica, Via Ferrata, 1, 27100 Pavia, Italia
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     title = {Stability estimates for certain {Faber-Krahn,} isocapacitary and {Cheeger} inequalities},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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Fusco, Nicola; Maggi, Francesco; Pratelli, Aldo. Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 8 (2009) no. 1, pp. 51-71. http://archive.numdam.org/item/ASNSP_2009_5_8_1_51_0/

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