of linear PDE, and with N. Dencker and Zworski ([@DeSjZw]) we were able to find quite general results closely related to the classical topic of subellipticity for pseudodifferential operators of principal type, studied by Egorov, Hörmander and others. See [@Ho]. This topic in turn is closely related to the oblique derivate problem and degenerate elliptic operators, where V.G. Maz’ya has made important contributions. See [@Maz1; @Maz2].

In [@DeSjZw] we obtained resolvent estimates at certain boundary points,\
(A) under a non-trapping condition,\
and\
(B) under a stronger “subellipticity condition”.

In case (A) we could apply quite general and simple arguments related to the propagation of regularity and in case (B) we were able to adapt general Weyl-Hörmander calculus and Hörmander’s treatment of subellipticity for operators of principal type ([@Ho]). In the first case we obtained that the resolvent extends and has temperate growth in $1/h$ in discs of radius ${\cal O}(h\ln 1/h)$ centered at the appropriate boundary points, while in case (B) we got the corresponding extension up to distance ${\cal O}(h^{k/(k+1)})$, where the integer $k\ge 2$ is determined by a condition of “subellipticity type”.

However, the situation near boundary points of the type (B) is more special than the general 