Journal of Convex Analysis, Vol. 5, No. 1, pp. 1-17 (1998)

Non-Coercive Variational Problems with Constraints on the Derivatives

Cristina Marcelli

Dipartimento di Matematica, Universita di Perugia, Via L. Vanvitelli 1, 06123 Perugia, Italy,

Abstract: We establish a necessary and sufficient condition for the existence of the minimum of the functional $\dis{\int_0^1} f(t,v^\prime(t))dt$ in the class ${\cal W}_d^p=\{v\in W^{1,p}([0,1]): v(0)=0, v(1)=d, v^\prime(t) \geq \alpha\}$, in terms of a limitation of the slope  $d$. Some applications to quasi-coercive and non-coercive integrands are also derived.

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