Inequalities between Dirichlet and Neumann eigenvalues
Consider a smooth enough bounded open set D in \({\mathbb{R}}^ n\) and \(\{\lambda_ k\}\) (resp. \(\{\mu_ k\})\) the eigenvalues of: \(\Delta u+\lambda u=0\) for Dirichlet (resp. Neumann) problem. The authors prove inequalities of the form: \(\mu_{k+R}<\lambda_ k\) for \(k\geq 1.\) In particular if D is convex they obtain: \(\mu_{k+n}<\lambda_ k\) for \(k\geq 1\).
scientific article; zbMATH DE number 3983738