$6\mathrm{.}42.$ Consider the functions $u_1=x^2-y^2$ and $u_2=x^2-y^2+(x^2+y^2-1)$ defined on a disk of radius $1.$

Verify the first is harmonic but the second is not.

Verify they both satisfy the same boundary condition on the circle radius one: $1,.$

Compute energy ${}_W||gradu|{|}^{2}dA$ of the following $u-$functions. Verify that the first function's energy is less than the second.