WIAS Preprint No. 1203, (2007)

Elliptic model problems including mixed boundary conditions and material heterogeneities


  • Haller-Dintelmann, Robert
  • Kaiser, Hans-Christoph
  • Rehberg, Joachim

2010 Mathematics Subject Classification

  • 35B65 35J25 35R05


  • Elliptic transmission problems, mixed boundary problems, $W^1,p$ regularity


We present model problems in three dimensions, where the operator $-nabla cdot mu nabla$ maps the Sobolev space $W^1,p_Gamma(Omega)$ isomorphically onto $W^-1,p_Gamma(Omega)$ for a $p>3$. The emphasis is here on the case where different boundary conditions meet material heterogeneities.

Appeared in

  • J. Math. Pures Appl., 89 (2008) pp. 25--48.

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