Abstract

As a vague and general principle, the observable states of systems we consider in nature are the ones that minimize some energy or that are critical points of this energy. The object of calculus of variations is to prove existence of minimizers and critical points, of such energies and to study the properties of these minimizers trying to describe them as precisely as possible. That is why numerous phenomena in physics, biology, economy and other fields can be described with the help of calculus of variations and partial differential equations (PDEs).