Shapiro–Lopatinskii ellipticity

We now define the notion of Shapiro–Lopatinskii ellipticity (also known as SLellipticity) of boundary conditions for an operator in Boutet de Monvel’s calculus on a smooth manifold X with boundary Y . The results can be found, for instance, in the monograph [34] of Rempel and Schulze, and of course, also in the work [9] of Boutet de Monvel; see also the monograph of Grubb [19]. Therefore, here we only sketch the proofs.