Reverse Faber-Krahn and Szegő-Weinberger type inequalities for annular domains under Robin-Neumann boundary conditions

Abstract

We prove Szego-Weinberger inequality for problems with mixed boundary conditions of the Robin-Neumann boundarytype. We deal with higher eigenvalues and study the symmetries and nonradiality of the eigenfunctions. We also discuss the validity of the Payne conjecture for some special type of domains.