Lyapunov-type inequalities for partial differential equations

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 Ap 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.