×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI