Many phenomena in physics can be formulated by boundary value problems for linear,  elliptic partial differential equations. The prototype of a mixed boundary value problem for the Laplacian is the Poisson problem on a polygon with partly Dirichlet and partly Neumann boundary conditions. A very large number of papers were published about boundary value   problems on singular domains, among which the papers of Kondratiev  and Mazya-Plamenevskij  have played a pioneering role. We want to study such problems for a wider set of singularities and in higher-dimensional contexts from a geometric point of view. The basic idea is to use a conformal blow-up to transfer the problem from singular spaces on weighted regularity scales to noncompact spaces with uniform regularity scales.