I came across the following "functional" at work:
$$ \Pi [b]=\iint_0^{\lambda b(v,\lambda)} vf(v,\lambda) \; dv \; d\lambda $$
it's part of an optimization problem that tries to find $b$, subject to some constraints on $b$.
I'm not familiar with that type of integral, where the solution function is actually in one of the bounds of the integral. Is there a specific name for that type of integral? Would the calculus of variations address that type of optimization problem? Or is there a field of functional analysis (calculus?) that would address it?
Thanks!
