On the Velocities of Lagrangian Minimizers
نویسندگان
چکیده
We consider minimizers for the natural time-dependent Lagrangian system in R with Lagrangian L(x, v, t) = |v|/β − U(x, t), where β > 1. For minimizers on a time interval of length T with one endpoint fixed, we prove that the absolute values of velocities are bounded by K log T , provided that the potential U(x, t) and its gradient are uniformly bounded. We also show that the above estimate is asymptotically sharp. 2000 Math. Subj. Class. 37J50.
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