Euler Lagrange Equation for higher

Dear all,

the Euler-Lagrange equation for a functional

J(u) = int_a^b F(u(x)) dx

is

d/du F = 0,

if F is a function from R -> R and u is a function R -> R.
My question is: how does the EL EQ look like if u is a function R^2 ->
R^2 and F a function of R^2 to R?

Thanks for your help!
.