We establish a necessary and sufficient condition for the existence of the minimum of the functional \int_a^b f(t, v' (t))dt in the class W = {v \in W^{1,p}([a, b]): v(a) =0, v(b) = d}, in terms of a limitation on the slope d. We derive some applications regarding quasi-coercive and non-coercive integrands.
One-dimensional non-coercive problems of the Calculus of Variations / Marcelli, Cristina. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 173:1(1997), pp. 145-161.
One-dimensional non-coercive problems of the Calculus of Variations
MARCELLI, Cristina
1997-01-01
Abstract
We establish a necessary and sufficient condition for the existence of the minimum of the functional \int_a^b f(t, v' (t))dt in the class W = {v \in W^{1,p}([a, b]): v(a) =0, v(b) = d}, in terms of a limitation on the slope d. We derive some applications regarding quasi-coercive and non-coercive integrands.File in questo prodotto:
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