Abstract

We establish a necessary and sufficient condition for the existence of the minimum of the functional ∫₀¹ f(t, v′(t))dt in the class Wdp={v∈W1,p([0,1]):v(0)=0,v(1)=d,v′(t)≥α}\mathcal{W}^p_d = \{v \in W^{1,p}([0,1]) : v(0) = 0, v(1) = d, v'(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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Cristina Marcelli

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

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Suggested citation

C. Marcelli. “Non-Coercive Variational Problems with Constraints on the Derivatives.” Journal of Convex Analysis 5 (1998), No. 1, 1–17. https://doi.org/10.68381/jca05-1

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Published by Heldermann Verlag, 1998. Rights now held by Banach Press LLC.