Legendre transformations and Clairaut-type equations
  It is noted that the Legendre transformations in the standard formulation of quantum field theory have the form of functional Clairaut-type equations. It is shown that in presence of composite fields the Clairaut-type form holds after loop corrections are taken into account. A new solution to the functional Clairaut-type equation appearing in field theories with composite fields is found. 
Peter M. Lavrov, Boris S. Merzlikin
hep-th math-ph math.MP