Some Examples of Crinkles
Many physical problems can be phrased as the problem of minimizing some energy functional E[f] over a given class of admissible functions f. It can happen that there is a minimizing sequence fn that approaches a limit f̄ but f̄ does not minimize E, either because f̄ is not in the admissible class or because E is not lower semicontinuous. In the examples that I discuss here, this happens because the derivatives <Inline>#</Inline> are highly discontinuous and do not approach f̄’ in the limit. I call such sequences crinkles, and call the limiting function f̄ the carrier of the crinkle. Young  has written a book on the subject; he calls such sequences generalized curves. In control theory the same sort of thing is also called a chattering state.
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