Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems. Issue 1 (30th January 2015) - Brandolini, Barbara; Chiacchio, Francesco; Trombetti, Cristina
Abstract : In this paper we prove a sharp lower bound for the first non-trivial Neumann eigenvalue μ 1 ( Ω ) for the p -Laplace operator ( p > 1) in a Lipschitz bounded domain Ω in ℝ n . Our estimate does not require any convexity assumption on Ω and it involves the best isoperimetric constant relative to Ω . In a suitable class of convex planar domains, our bound turns out to be better than the one provided by the Payne—Weinberger inequality.