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problem in problem

(1/1)

Jingxuan Zhang:
I assume problem 2.1 of http://www.math.toronto.edu/ivrii/PDE-textbook/Chapter10/S10.P.html intends to ask "Minimizing T" subject to no constrain?

Victor Ivrii:
No constrains affecting L.-E. equations,

(A) but there is a constrain  $u(0)=0$, $u(a)=h$

(B) In fact, one can remove the last constrain.
With (A) we are looking for the fastest slide between two points (so given are horizontal projection and the difference in heights)
With (B) only horizontal projection..

http://mathworld.wolfram.com/BrachistochroneProblem.html