= Bounded Dirichlet uniqueness in a quadrant
Two bounded <harmonic functions> continuous to the quadrant edges with the same <Dirichlet boundary conditions> are equal. Their difference is bounded and zero on both axes. <Odd reflection> across each axis gives a bounded harmonic extension away from the corner; the <removable singularity for a bounded harmonic function> fills in that corner. The <harmonic Liouville theorem> makes that extension constant, and oddness makes the constant zero. This does not exclude unbounded examples such as the <zero-boundary harmonic growth in a quadrant>.
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