1. ## Minimum of Functional

Find an upper bound for the minimum of the functional
$J\{y\} = \int\begin{array}{cc}1\\0\end{array} y^2 y'^2 dx$
subject to y(0)=0 and y(1)=1 using te trial functions
$y_\epsilon(x)=x^\epsilon$ with $\epsilon > 1/4.$ Justify your argument.

2. So, what have you done so far?

Incidentally, while I grant you that this is calculus of variations, it really belongs in the Advanced Applied Mathematics forum. If you report your own post and ask the mods to move it, they'll do that for you. That's the correct way to move the post.

3. Originally Posted by pdnhan
Find an upper bound for the minimum of the functional
$J\{y\} = \int\begin{array}{cc}1\\0\end{array} y^2 y'^2 dx$
subject to y(0)=0 and y(1)=1 using te trial functions
$y_\epsilon(x)=x^\epsilon$ with $\epsilon > 1/4.$ Justify your argument.

If you minimise $J\{y_{\epsilon}\}$ wrt $\epsilon$ you will have an upper bound on the mininmum of the functional. This is a standard (constrained) minimisation problem.

CB

4. Originally Posted by Ackbeet
So, what have you done so far?

Incidentally, while I grant you that this is calculus of variations, it really belongs in the Advanced Applied Mathematics forum. If you report your own post and ask the mods to move it, they'll do that for you. That's the correct way to move the post.
'fraid not, this is a plain old calculus problem, when interpreted.

CB

5. I got it now, thank you very much!