A function f(x,y) is defined as subharmonic in a region R if 2 f 0

Question:

A function f(x,y) is defined as subharmonic in a region R if ∇²f ≥ 0 at all points in R. It can be proved that the maximum value of a subharmonic function occurs only on the boundary S of region R. For the torsion problem, show that the square of the resultant shear stress τ,² = τ,²_xz + τ,²_yz is a subharmonic function, and thus the maximum shear stress will always occur on the section boundary.