A note on absolute extrema of certain integrals
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Abstract This note deals with a method for finding functions with prescribed endpoints which yield the absolute extrema (minima or maxima) of certain integrals. The technique described below differs from the theory of the variational calculus in two important respects; it leads to an absolute extremum of the given integral and it does so directly , i.e. without a variational argument based on a comparison of neighboring functions.
[1] Oskar Bolza,et al. Vorlesungen uber Variationsrechnung , 1961 .