Variational Dual Solutions of PDE

Equations not arising from a variational principle, as well as ones that arise from functionals that are not bounded above or below, can be endowed with one with favorable properties. The concept, and some examples are listed below:

The basic idea

Variational dual solutions for nonlinear elasticity

Variational dual solutions for incompressible fluids

Variational dual solutions for Chern-Simons theory

Variational dual solutions for (inviscid) Burgers equation