Calculus of Variations and Geometric Measure Theory

G. Cupini - M. Guidorzi - C. Marcelli

Necessary conditions and non-existence results for autonomous nonconvex variational problems

created by cupini on 23 May 2007
modified on 15 Nov 2007


Published Paper

Inserted: 23 may 2007
Last Updated: 15 nov 2007

Journal: J. Differential Equations
Volume: 243
Pages: 329-348
Year: 2007


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