At time 05:10 in the video it seems like the closed interval [ \zeta - \delta, \zeta + \delta ] should be an open interval ( \zeta - \delta, \zeta + \delta ) since \psi(x) > 0 at the two end points. To me it appears to break the continuity of \psi(x) at the endpoint whereas if this was an open interval it would be OK because \psi would equal zero at the endpoints and when you are in the interior of the open interval then \psi would approach zero as you get closer to the endpoints? Thanks for the great video series!
This series is pure gold! Btw, could you provide some reference to online material where I can find the sufficient condition for extremizing I(u) on this kind of problems?
At time 05:10 in the video it seems like the closed interval [ \zeta - \delta, \zeta + \delta ] should be an open interval ( \zeta - \delta, \zeta + \delta ) since \psi(x) > 0 at the two end points. To me it appears to break the continuity of \psi(x) at the endpoint whereas if this was an open interval it would be OK because \psi would equal zero at the endpoints and when you are in the interior of the open interval then \psi would approach zero as you get closer to the endpoints? Thanks for the great video series!
Can we have some hinted exercices in general cases u(x) with x in R^n and u too in R^n .What could the Euler-Lagrange first formula ?
Great! a lot of thanks
This series is pure gold! Btw, could you provide some reference to online material where I can find the sufficient condition for extremizing I(u) on this kind of problems?