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.
G. Cupini, M. Guidorzi, C. Marcelli (2007). Necessary conditions and non-existence results for autonomous nonconvex variational problems. JOURNAL OF DIFFERENTIAL EQUATIONS, 243, 329-348 [10.1016/j.jde.2007.05.035].
Necessary conditions and non-existence results for autonomous nonconvex variational problems
CUPINI, GIOVANNI;
2007
Abstract
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.File in questo prodotto:
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