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Oct 30, 2009 at 1:59 comment added Deane Yang It is my understanding that this was Dirichlet's original argument, but he had no rigorous way to prove that a limit of a minimizing sequence exists. Only much later, could existence, uniqueness, and regularity (which is also important) could be proved.
Oct 29, 2009 at 17:21 history answered Julián Aguirre CC BY-SA 2.5