Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities

Fusco, Nicola; Maggi, Francesco; Pratelli, Aldo

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 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.

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