1. Classical convex variational problems and their Euler-Lagrange equations
2. Self-dual Lagrangians and monotone vector fields
3. Self-dual variational calculus for non Euler-Lagrange PDEs and parabolic equations driven by convex energies
4. Self-dual variational calculus, inverse problems and control theory
5. Self-dual variational calculus and homogenization
6. Anti-symmetric Hamiltonians and non-linear PDEs and evolution equations, including Navier-Stokes type equations
7. Anti-symmetric Hamiltonians and invariant mass transport problems
8. Non-convex self-dual variational calculus and Hamiltonian systems

References:

1. N. Ghoussoub: Self-dual Partial Differential Systems and Their Variational Principles, Springer Monographs in Mathematics, Springer New York (2008)
2. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. Classics Appl. Math 28, SIAM, 1999.