Mixed boundary value problems and parametrices in the edge calculus

Mixed elliptic boundary value problems are characterised by conditions which have a jump along an interface of codimension 1 on the boundary. We study such problems in weighted edge spaces and show the Fredholm property and the existence of parametrices under additional conditions of trace and potential type on the interface. We develop a new method for computing the interface conditions in terms of the index of boundary value problems in weighted spaces on infinite cones, combined with structures from the calculus of boundary value problems on a manifold with edges. This will be illustrated by the Zaremba problem and other mixed problems for the Laplace operator. The approach itself is completely general.