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I have read that the boundary condition can be parameterized as

[tex] x=\sigma, \qquad y=(1-\sigma^2)^{1/2}, \qquad u=1.[/tex]

My question is this: couldn't we also have [itex]y=-(1-\sigma^2)^{1/2}[/itex]?? Don't we have to assume that it could be either the positive or negative square root ([itex] y = \pm\sqrt{1-x^2} [/itex])?