Calculus of Variations and Geometric Measure Theory

N. Fusco - F. Maggi - A. Pratelli

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

created by maggi on 05 May 2007
modified by pratelli on 25 Sep 2010


Published Paper

Inserted: 5 may 2007
Last Updated: 25 sep 2010

Journal: Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)
Year: 2007


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.