Dipartimento di Matematica, Universita di Perugia, Via L. Vanvitelli 1, 06123 Perugia, Italy, marcelli@unipg.it
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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