Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems. Issue 1 (30th January 2015)

• Record Type: Journal Article
• Authors: Brandolini, Barbara; Chiacchio, Francesco; Trombetti, Cristina
• Is Part Of: Proceedings. Volume 145:Issue 1(2015)
• Page Start: 31
• Page End: 45
• Publication Date: 2015-01-30
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210513000371
• Languages: English
• ISSNs: 0308-2105

Abstract

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.