Problem 5. 20 Marks
Given the variational problem
$\int[a_1(\partial_1 v)^2 + a_2(\partial_2 v)^2 + a_3(\partial_1 v - \partial_2 v)^2 - 2fv]dx \to min!$
with $a_1, a_2, a_3 > 0$, find the associated Euler differential equation and the
difference star, using the same form of approximating function as in Example
4.3 (on page 56 of the prescribed book).