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.
Necessary conditions and non-existence results for autonomous nonconvex variational problems / G. CUPINI; GUIDORZI M; MARCELLI C. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 243:(2007), pp. 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.
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