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Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities. (English) Zbl 1176.49047
Summary: 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.

##### MSC:
 49R05 Variational methods for eigenvalues of operators 35J20 Variational methods for second-order elliptic equations 49J40 Variational inequalities 26D20 Other analytical inequalities
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