Abstract :
We prove Harnack’s inequality for first eigenfunctions of the p-Laplacian in metric measure spaces. The
proof is based on the famous Moser iteration method, which has the advantage that it only requires a weak
(1,p)-Poincaré inequality. As a by-product we obtain the continuity and the fact that first eigenfunctions
do not change signs in bounded domains.
© 2005 Elsevier Inc. All rights reserved
Keywords :
First eigenfunction , Harnack’s inequality , Metricspace , Nonlinear eigenvalue problem , Newtonian space , Poincaré inequality , Rayleigh quotient , Caccioppoli estimate , First eigenvalue , doubling measure , Sobolev space , Superminimizer , Minimizer
