TURNER, LINCOLN HULLEY

The purpose of this thesis is to examine certain properties of integrals used in the calculus of variations, particularly the pro- perty of lower semi-continuity. To do this, a new form of the Weier- strass integral on continuous parametric rectifiable curves and a new integral on continuous parametric surfaces have been defined. This second integral is shown to be equivalent to an integral defined recently by L. Cesari. Theorems giving sufficient conditions for an integral to be lower semi-continuous are proved which are more general than any given before

THE DIRECT METHOD IN THE CALCULUS OF VARIATIONS

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