${W}^{1,q}$ regularity results for elliptic transmission problems on heterogeneous polyhedra
Please always quote using this URN:urn:nbn:de:0296-matheon-4590
- Let $\Upsilon$ be a three-dimensional Lipschitz polyhedron, and assume that the matrix function $\mu$ is piecewise constant on a polyhedral partition of $\Upsilon$. Based on regularity results for solutions to two-dimensional anisotropic transmission problems near corner points we obtain conditions on $\mu$ and the intersection angles between interfaces and $\partial \Upsilon$ ensuring that the operator $-\nabla \cdot \mu \nabla$ maps the Sobolev space $W^1,q_0(\Upsilon)$ isomorphically onto $W^-1,q(\Upsilon)$ for some $q > 3$.