ABSTRACT
The Lagrange identity method gives interesting identities governing the solutions of certain classes of partial differential equations, linear ones as hitherto developed, under suitable boundary conditions; the method is applicable to some other equations also, including integral equations. In its simplest manifestation, it depends on two sets of integration by parts. It hinges crucially on the notion of a symmetric operator whose defining symmetry property is often styled a Lagrange identity. The method is introduced by applying it to two simple partial differential equations, one a diffusion equation, the other a wave equation or Laplace type equation, under homogeneous boundary conditions. The Lagrange identity method is generally attributed to Brun who was the first to use it in the context of elastodynamics.
