= Zero-boundary harmonic growth in a quadrant
The <harmonic function> $v(x,y)=xy$ vanishes on both axes but is nonzero in the quadrant, and $v_z=-iz/2$. More generally $\operatorname{Im}z^{2m}$, for a positive integer $m$, vanishes on both axes and is harmonic. Adding these unbounded functions leaves all edge <Dirichlet boundary conditions> unchanged. Thus decay of the boundary data does not imply decay of every solution, and an edge-data-only formula cannot determine an arbitrary solution's <Wirtinger derivative>. A boundedness or suitable growth condition must select the solution.
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