In the classical calculus of variations it is know that a necessary condition to a minimum of a functional $$\int_0^T L(x,\dot{x},t)dt$$ is the Legendre condition $$L_{\dot x \dot x} \geq 0.$$ If the inequality is strong, then the theory is further developed into the Jacobi's theory of conjugate points.

I am interested in the case when the inequality is not strict, but $L_{\dot x\dot x} = 0$ in an isolated point. Are there any known second order minimality conditions in that case?

Thank you.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.