Inserted: 23 may 2007
Last Updated: 15 nov 2007
Journal: J. Differential Equations
Classical one-dimensional, autonomous Lagrange problems are considered. In absence of any smoothness, convexity or coercivity condition on the energy density, we prove a DuBois-Reymond type necessary condition, expressed as a differential inclusion involving the subdifferential of Convex Analysis. As a consequence, a non-existence result is obtained.
Keywords: autonomous variational problem, necessary condition, DuBois-Reymond condition, non-existence result