PDE Seminar Abstracts

Some recent estimates on linear Neumann eigenvalues and eigenfunctions

Barbara Brandolini
University of Naples
17 Aug 2009 3-4pm, Carslaw Room 454


We prove a reverse Holder inequality for the first nontrivial eigenfunction of the Neumann Laplacian. From this we deduce a lower bound for the first nontrivial eigenvalue in terms of the isoperimetric constant relative to the domain. We finally show that our results are asymptotically sharp at least in dimension two.