The first eigenvalue of p-Laplacian and geometric estimates
Abimbola Abolarinwa · Nonlinear Analysis and Differential Equations · 2014
Copyright c © 2014 Abimbola Abolarinwa. This is an open access article distributed un-der the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We investigate the nonlinear eigenvalue problem for the p-Laplacian on compact manifold with zero boundary condition. In particular, we obtain classical estimates of Faber-Krahn inequality and Cheeger-type inequality for the first eigenvalue. As an application we derive Mckean-type estimate and discuss some geometric estimates involving the Lp-Sobolev constants.