(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Haller-Dintelmann, Robert; Kaiser, Hans-Christoph; Rehberg, Joachim
We characterise the singularities of elliptic div-grad operators at
points or edges where several materials meet on a Dirichlet or Neumann part
of the boundary of a two- or three-dimensional domain. Special emphasis is
put on anisotropic coefficient matrices. The singularities can be computed as
roots of a characteristic transcendental equation. We establish uniform
bounds for the singular values for several classes of three- and fourmaterial
edges. These bounds can be used to prove optimal regularity results for
elliptic div-grad operators on three-dimensional, heterogeneous, polyhedral
domains with mixed boundary conditions. We demonstrate this for the benchmark
Lshape problem.
