Inserted: 5 may 2007
Last Updated: 25 sep 2010
Journal: Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)
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 the can be easily adapted to treat also certain isocapacitary and Cheeger inequalities.