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MR1357405 (98d:49048) 49N60 (49J30 49K30)
Sychev, M. A.; Mizel, V. J. A condition on the value function both necessary and sufficient for full regularity of minimizers of one-dimensional variational problems. Trans. Amer. Math. Soc. 350 (1998), no. 1, 119–133.
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