Lyapunov-type Inequalities for Partial Differential Equations

2013/04/25 by Pablo L. De Nápoli, De Nápoli, Pablo L., Juan P. Pinasco +1
Mathematics · #35P15 #35P30 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35P15 #msc:35P30

paper · pdf · doi:10.48550/arxiv.1304.6988

arxiv created 2013/04/25 · arxiv updated 2013/04/26

Abstract

In this work we present a Lyapunov inequality for linear and quasilinear elliptic differential operators in N-dimensional domains Ω. We also consider singular and degenerate elliptic problems with A_p coefficients involving the p-Laplace operator with zero Dirichlet boundary condition. As an application of the inequalities obtained, we derive lower bounds for the first eigenvalue of the p-Laplacian, and compare them with the usual ones in the literature.

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