For solutions vanishing on the boundary of the Heisenberg half-space, a weighted |x|^2 bound on the source gives linear-in-t growth and a d^(2+alpha) second-order expansion at the characteristic point.
Apushkinskaya and Alexander I
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Boundary regularity for subelliptic equations in the Heisenberg group
For solutions vanishing on the boundary of the Heisenberg half-space, a weighted |x|^2 bound on the source gives linear-in-t growth and a d^(2+alpha) second-order expansion at the characteristic point.