In this paper we first present a definition of weak local extremum for the functionals I[x] of the CoV both in the case in which x′ is assumed to be essentially bounded and in the case in whichx'is allowed to be unbounded. Then we obtain a form of the DuBois-Reymond necessary condition known in the case of strong local extrema of the CoV. Interesting counterexamples complete the work and illustrate the natural framework introduced in the paper.
A remark on the classical DuBois-Reymond necessary condition for weak local extrema
PUCCI, Patrizia
1982
Abstract
In this paper we first present a definition of weak local extremum for the functionals I[x] of the CoV both in the case in which x′ is assumed to be essentially bounded and in the case in whichx'is allowed to be unbounded. Then we obtain a form of the DuBois-Reymond necessary condition known in the case of strong local extrema of the CoV. Interesting counterexamples complete the work and illustrate the natural framework introduced in the paper.File in questo prodotto:
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