6533b81ffe1ef96bd12771b8
RESEARCH PRODUCT
Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems
Barbara BrandoliniFrancesco ChiacchioCristina Trombettisubject
Pure mathematicsp-Laplace operatorGeneral MathematicsMathematics::Spectral TheoryLipschitz continuityUpper and lower boundsDomain (mathematical analysis)ConvexityCombinatoricslower boundsMathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaBounded functionFOS: MathematicsNeumann eigenvalueIsoperimetric inequalityLaplace operatorEigenvalues and eigenvectorsMathematicsAnalysis of PDEs (math.AP)description
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-02-07 |