Lyapunov-type inequalities for partial differential equations

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.