Excerpt from Researches in the Calculus of Variations, Principally on the Theory of Discontinuous Solutions: An Essay to Which the Adams Prize Was Awarded in the University of Cambridge in 1871
The subject of this Essay was prescribed in the following terms by the Examiners:
The Adams Prize.
A determination of the circumstances under which discontinuity of any kind presents itself in the solution of a problem of maximum or minimum in the Calculus of Variations, and applications to particular instances.
It is expected that the discussion of the instances should be exemplified as far as possible geometrically, and that attention be especially directed to cases of real or supposed failure of the Calculus.
It was after much hesitation that I resolved to discuss the subject; the fact that it had given rise to some controversy, however, naturally led me to enforce what I believed to be the correct and adequate explanation of the difficulties which had been raised.
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