  We prove weighted anisotropic analytic estimates for solutions of second
order elliptic boundary value problems in polyhedra. The weighted analytic
classes which we use are the same as those introduced by Guo in 1993 in view of
establishing exponential convergence for hp finite element methods in
polyhedra. We first give a simple proof of the known weighted analytic
regularity in a polygon, relying on a new formulation of elliptic a priori
estimates in smooth domains with analytic control of derivatives. The technique
is based on dyadic partitions near the corners. This technique can successfully
be extended to polyhedra, providing isotropic analytic regularity. This is not
optimal, because it does not take advantage of the full regularity along the
edges. We combine it with a nested open set technique to obtain the desired
three-dimensional anisotropic analytic regularity result. Our proofs are global
and do not require the analysis of singular functions.
