$W^1,q$ regularity results for elliptic transmission problems on heterogeneous polyhedra
- Elschner, Johannes
- Kaiser, Hans-Christoph
- Rehberg, Joachim
- Schmidt, Gunther
2010 Mathematics Subject Classification
- 35B65 35J25 35Q40 35R05
- Elliptic transmission problems, polyhedral domains, $W^1q$ regularity
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 $q > 3$.
- Math. Models Methods Appl. Sci., 17 (2007) pp. 593--615.