Abstract
In the investigation of variational problems associated with functionals of the form (*), lower semi-continuity properties of the functionals play an important role. These properties are strongly related to certain convexity properties of the integrand f. In many variational problems of non-parametric type, the integrand f is convex with respect to px. Such problems were investigated by Tonelli, Cesari, Morrey, Serrin and others. The assumption that f is convex with respect to 0,, makes it possible to obtain very strong lower semi-continuity theorems for If. Results of this type, under very general conditions, were obtained by Serrin [11].
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