In this paper we prove a sharp lower bound for the first non-trivial Neumann eigenvalue μ1(Ω) for the p-Laplace operator (p < 1) in a Lipschitz bounded domain Ω in Rn. 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.
Brandolini B., Chiacchio F., Trombetti C. (2015). Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS, 145(1), 31-45 [10.1017/S0308210513000371].
Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems
Brandolini B.
;
2015-01-01
Abstract
In this paper we prove a sharp lower bound for the first non-trivial Neumann eigenvalue μ1(Ω) for the p-Laplace operator (p < 1) in a Lipschitz bounded domain Ω in Rn. 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.
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