W1,q REGULARITY RESULTS FOR ELLIPTIC TRANSMISSION PROBLEMS ON HETEROGENEOUS POLYHEDRA
Johannes Elschner, H.–Ch. Kaiser, Joachim Rehberg, G. SCHMIDT · Mathematical Models and Methods in Applied Sciences · 2007
Let ϒ be a three-dimensional Lipschitz polyhedron, and assume that the matrix function μ is piecewise constant on a polyhedral partition of ϒ. Based on regularity results for solutions to two-dimensional anisotropic transmission problems near corner points we obtain conditions on μ and the intersection angles between interfaces and ∂ϒ ensuring that the operator -∇ · μ∇ maps the Sobolev space [Formula: see text] isomorphically onto W-1,q(ϒ) for some q > 3.