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Minimal Surface and Boundary Equation

Please see the attached file for the fully formatted problems.

Show that
Z(x, y) = ln(sin y/sin x)

is a solution to the minimal surface equation.
(1 + Z)Z1 + 2ZXZZX + (1 + Z)Z = 0,
in the region 0 < x < ir, 0 < y < pi. What happens on the boundary of this region? Suppose we consider a constant multiple of Z(x, y) ? is it still a solution of the PDE?

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Solution Summary

A minimum surface equation is investigated. The solution is detailed and well-presented.

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