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Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.

1 vote

proving the existence of a minimizer of this functional

I haven't verified your calculation of the E-L equation. But if the Jacobi-field equation (second variation) is degenerate then you have to show that $A[f+g] \leq A[f]$ for either all $g$ or, endowing …
dcs24's user avatar
  • 213
2 votes

Minimizing action squared versus action

I believe that the equivalence of minimisers follows if and only if when $r$ is a critical of $A$ it holds that $L(r,r') = C \in \mathbb R, \forall x \in \Omega$. The idea being inspired by the equiva …
dcs24's user avatar
  • 213