Geometric operators on singular domains

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.


    Team Members

    Prof. Dr. Bernd Ammann
    Project leader
    Universität Regensburg

    JProf. Dr. Nadine Große
    Project leader
    Albert-Ludwigs-Universität Freiburg im Breisgau

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