On reverse Faber-Krahn inequalities
T. V. Anoop and K. Ashok Kumar
Journal of Mathematical Analysis and Applications
In 1961, Payne-Weinberger showed that â€˜among the class of membranes with given area A, free along the interior boundaries and fixed along the outer boundary of given length L0, the concentric annulus has the highest fundamental frequency.â€™ We extended this result for the first eigenvalue of p-Laplacian (pâˆˆ(1,âˆž)) in higher dimensional domains whose outer boundary is a fixed sphere. As an application, we prove that the nodal set of the second eigenfunctions of p-Laplacian (with mixed boundary conditions) on a ball cannot be a concentric sphere.