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

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.
Settore MAT/05 - Analisi Matematica
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/493961
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