Elimination of Hamilton-Jacobi equation in extreme variational problems

Details Elimination of Hamilton-Jacobi equation in extreme variational problems Elimination of Hamilton-Jacobi equation in extreme variational problems

2010-08-16

arxiv.org/abs/1008.2599v1

Mathematics

Optimization and Control

10 pages

Scientific paper

It is shown that extreme problem for one-dimensional Euler-Lagrange variational functional in $C^1[a;b]$ under the strengthened Legendre condition can be solved without using Hamilton-Jacobi equation. In this case, exactly one of the two possible cases requires a restriction to a length of $[a;b]$, defined only by the form of integrand. The result is extended to the case of compact extremum in $H^1[a;b]$.

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