On the existence and uniqueness of minima and maxima on spheres of the integral functional of the calculus of variations

Details On the existence and uniqueness of minima and maxima on spheres of the integral functional of the calculus of variations On the existence and uniqueness of minima and maxima on spheres of the integral functional of the calculus of variations

2005-10-10

arxiv.org/abs/math/0510191v3

Mathematics

Optimization and Control

Scientific paper

We deal with the integral functional of the calculus of variations assuming
that the gradient of the integrand is Lipschitzian. We then prove that if this
gradient does not vanish at zero, then the functional has a unique minimum and
a unique maximum on each sphere, centered at zero, with radius small enough.

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