PORTUGALIAE MATHEMATICA Vol. 55, No. 2, pp. 167185 (1998) 

Existence of Minimizers for Some Non Convex OneDimensional IntegralsNicola Fusco, Paolo Marcellini and António OrnelasAbstract: We consider integrals of the type $\int_{a}^{b}\{h(u')+g(u)\}\,dx$, where $h$ is a nonconvex function such that $h^{**}(0)=h(0)$. It is still not known whether this condition alone on $h$ is sufficient to get existence of minimizers for general $g$. In this paper we prove it under very mild assumptions on $g$, e.g. it can be any combination of elementary functions. Keywords: Calculus of variations; nonconvex integrals. Classification (MSC2000): 49J05, 49K05, 49M20 Full text of the article:
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