Asymptotics of potentials in the edge calculus
David Kapanadze, Bert‐Wolfgang Schulze · publish.UP (University of Potsdam) · 2006
Abstract. Boundary value problems on manifolds with conical singularities or edges contain potential operators as well as trace and Green operators which play a similar role as the corre-sponding operators in (pseudo-differential) boundary value problems on a smooth manifold. There is then a specific asymptotic behaviour of these operators close to the singularities. We characterise potential operators in terms of actions of cone or edge pseudo-differential operators (in the neighbouring space) on densities supported by submanifolds which also have conical or edge singularities. As a byproduct we show the continuity of such potentials as continuous operators between cone or edge Sobolev spaces and subspaces with asymptotics. Key words: Surface potentials with asymptotics, edge Sobolev spaces, operators on mani-folds with conical and edge singularities