On upper bounds for high order Neumann eigenvalues of convex domains in Euclidean space

Pawel Kröger
1999 Proceedings of the American Mathematical Society  
We derive sharp upper bounds for eigenvalues of the Laplacian under Neumann boundary conditions on convex domains with given diameter in Euclidean space. We use the Brunn-Minkowski theorem in order to reduce the problem to a question about eigenvalues of certain classes of Sturm-Liouville problems.
doi:10.1090/s0002-9939-99-04804-2 fatcat:mlwxej6fgjaerd3csie5irjvrq