Polyconvex Materials: Existence of Energy-Minimizing Deformations

Abstract

As already mentioned below Theorem , the derivation of Euler-Lagrange equations for the elasticity functional ${\mathcal E}$ is only formal and we cannot rely on the fact that minimizers of ${\mathcal E}$ satisfy these equations.

Nothing takes place in the world whose meaning is not that of some maximum or minimum.

Leonhard Paul Euler (1707–1783)