Microfunctions at the Boundary and Mild Microfunctions

Abstract

Let X be a real manifold, ℱ an object of Db(X), the derived category of the category of bounded complexes of sheaves of abelian groups on X. The functor μhom (•,•), defined in \[3], appears to be a useful tool especially in the theory of boundary value problems for partial differential equations. The aim of the present paper is to calculate the stalk of RΓzμ(NΩ, ℱ), when Ω is a convex (up to diffeomorphism) and open subset of a closed submanifold M of X, and Z is a closed convex proper cone of T\*X. As an application we show how to recover in a short and functorial way, the theory of mild microfunctions by Kataoka \[5].