Euler-Lagrange - Hi guys, is there a math genius/ prof or anyone able to solve that?

[zoca]

- Derive the Euler–Lagrange equations (including boundary conditions) for the minimal are problem defined by:

minJ = ∫_Ω √1+|∇u|² dΩ;

u(x;y) = u0(x;y); on δW;

where Ω is a bounded domain in R² with boundary δW

Thank you!

 

[Deleted member 4993]

- Derive the Euler–Lagrange equations (including boundary conditions) for the minimal are problem defined by:

minJ = ∫_Ω √1+|∇u|² dΩ;

u(x;y) = u0(x;y); on δW;

where Ω is a bounded domain in R² with boundary δW

Thank you!

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

 

[zoca]

Thanks answering

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

So I've basically no idea how to do it. I've never done that kind of problem. I know the Euler equation but I don't understand this. How to derive a gradient ∇, what do I do with this omega as a boundary, I'm in math at the university and no one in my class has been able to understand what to do yet. Of course I've read my theory...but there's nothing in it that helps me to solve this problem. Can you help? I don't even how long it would take to solve the problem.

Tank you