  The aim of this paper is to continue the study of asymptotic expansions and
summability in a monomial in any number of variables. In particular we
characterize these expansions in terms of bounded derivatives and we develop
tauberian theorems for the summability processes involved. Furthermore, we
develop and apply the Borel-Laplace analysis in this framework to prove the
monomial summability of solutions of a specific class of singularly perturbed
PDEs.
