Fusco, Nicola; Maggi, Francesco; Pratelli, Aldo Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities. (English) Zbl 1176.49047 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 8, No. 1, 51-71 (2009). 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. Cited in 47 Documents MSC: 49R05 Variational methods for eigenvalues of operators 35J20 Variational methods for second-order elliptic equations 49J40 Variational inequalities 26D20 Other analytical inequalities Keywords:first eigenvalue of the \(p\)-Laplacian; isocapacitary; Cheeger inequalities PDFBibTeX XMLCite \textit{N. Fusco} et al., Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 8, No. 1, 51--71 (2009; Zbl 1176.49047) Full Text: DOI