(Solved): Submission required. Let \( \Omega \) be the 2-D square domain \( 0 \leq x \leq H \), \( 0 \leq y \ ...

Submission required. Let \( \Omega \) be the 2-D square domain \( 0 \leq x \leq H \), \( 0 \leq y \leq H \). Consider the boundary value problem for \( u(x, y) \) on \( \Omega \) where \( u \) satisfies Laplace's equation and the following boundary conditions on the four sides: \( u(0, y)=0, u(x, 0)=0, u(H, y)=y^{3}, u(x, H)=x^{3} \). Does the function \( u(x, y)=x^{3} y^{3} / H^{3} \) solve this problem (why or why not)?