WIAS Preprint No. 1066, (2005)

$W^1,q$ 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 $q > 3$.

Appeared in

  • Math. Models Methods Appl. Sci., 17 (2007) pp. 593--615.

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