  The notion of microsupport and regularity for ind-sheaves was introduced by
M. Kashiwara and P. Schapira in "Microlocal study of ind-sheaves I:
microsupport and regularity". In this paper we study the behaviour of the
microsupport under several functorial operations and characterize
"microlocally" the ind-sheaves that are regular along involutive manifolds. As
an application we prove that if a coherent D-module M is regular along an
involutive manifold V (in the sense of "Systems of differential equations with
regular singularities and their boundary value problems") then the ind-sheaf of
temperate holomorphic solutions of M is regular along V. Another application is
the notion of microsupport for sheaves on the subanalytic site, which can be
given directly, without using the more complicated language of ind-sheaves.
