Elimination of Jacobi equation in extremal variational problems - Orlov, I. V. (Methods of Functional Analysis and Topology, 2011)
It is shown that the extremal problem for the one–dimensional Euler–Lagrange variational functional in C^1[a;b] under a strengthened Legendre condition can be solved without using the Jacobi equation. In this case, exactly one of the two possible cases requires a restriction to the length of [a;b], defined only by the form of the integrand. The result is extended to the case of compact extremum in H^1[a;b].