Lagrange's discrete model of the wave equation in dimension greater than one

Abstract

A celebrated theorem of Lagrange states that a solution of the wave equation with one-dimensional space variable is the uniform limit, as N tends to infinity, of a second order ODE obtained from a mechanical model discretizing a string as N identical harmonic oscillators. Answering to a question posed by G. Gallavotti we generalize this result to the case of any space dimension.