Microfunctions at the Boundary and Mild Microfunctions

Source abstract

Let X be a real manifold, \mathscr F an object of D^b(X) , the derived category of the category of bounded complexes of sheaves of abelian groups on X . The functor μ\hom (\cdot,\cdot) , 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 RΓ_zμ\hom(\boldsymbol N_Ω, \mathscr 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].