Lagrangian submanifolds and Hamilton-Jacobi equation
  Lagrangian submanifolds are becoming a very essential tool to generalize and geometrically understand results and procedures in the area of mathematical physics. Here we use general Lagrangian submanifolds to provide a geometric version of the Hamilton-Jacobi equation. This interpretation allows us to study some interesting applications of Hamilton-Jacobi equation in holonomic, nonholonomic and time-dependent dynamics from a geometrical point of view. 
M. Barbero-Li\~n\'an, M. de Le\'on, D. Mart\'in de Diego
math-ph math.MP