The first eigenvalue of the -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.
@article{ASNSP_2009_5_8_1_51_0, author = {Fusco, Nicola and Maggi, Francesco and Pratelli, Aldo}, title = {Stability estimates for certain {Faber-Krahn,} isocapacitary and {Cheeger} inequalities}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {51--71}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 8}, number = {1}, year = {2009}, mrnumber = {2512200}, zbl = {1176.49047}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2009_5_8_1_51_0/} }
TY - JOUR AU - Fusco, Nicola AU - Maggi, Francesco AU - Pratelli, Aldo TI - Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2009 SP - 51 EP - 71 VL - 8 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2009_5_8_1_51_0/ LA - en ID - ASNSP_2009_5_8_1_51_0 ER -
%0 Journal Article %A Fusco, Nicola %A Maggi, Francesco %A Pratelli, Aldo %T Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2009 %P 51-71 %V 8 %N 1 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2009_5_8_1_51_0/ %G en %F ASNSP_2009_5_8_1_51_0
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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