The Lipschitz continuity of Neumann eigenvalues on convex domains
Marty Ross · Hokkaido Mathematical Journal · 2004
We consider the Neumann spectrum of the Laplacian on convex domains. Radially parametrizing these domains, we show that each Neumann eigenvalue is Lipschitz continuous with respect to the sup norm on the radial functions.We use this to prove that each Neumann eigenvalue is maximized on the class of convex domains with fixed volume.