(a) State the value of and find where .
(b) A vector field is given by
where is a constant vector. Calculate the second-rank tensor using suffix notation and show how splits naturally into symmetric and antisymmetric parts. Show that
(c) Consider the equation
on a bounded domain subject to the mixed boundary condition
on the smooth boundary , where is a constant. Show that if a solution exists, it will be unique.
Find the spherically symmetric solution for the choice in the region for , as a function of the constant . Explain why a solution does not exist for