Otto Liess: Temperate growth at the boundary for solutions of hypoelliptic equations, p.283-295

In our main result we shall consider an hypoelliptic linear partial differential operator

with ${\mathcal C}^{\infty}$ coefficients defined on an open set

and consider a solution $u \in {\mathcal C}^{\infty} (U)$ of the equation

which extends to a distribution defined in a neighborhood of some point $x ^{0}$ in the boundary $\partial U$ of

. If hypoellipticity is a consequence of the existence of a suitable right parametrix of pseudodifferential type, then we shall show that

must have temperate growth at the boundary near $x ^{0}$ .