JournalsifbVol. 9, No. 2pp. 233–252

Optimal regularity for elliptic transmission problems including <em>C<sup>1</sup></em> interfaces

  • Johannes Elschner

    Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, Germany
  • Joachim Rehberg

    Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, Germany
  • Gunther Schmidt

    Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, Germany
Optimal regularity for elliptic transmission problems including <em>C<sup>1</sup></em> interfaces cover
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Abstract

We prove an optimal regularity result for elliptic operators μ:W01,qW1,q-\nabla \cdot \mu \nabla:W^{1,q}_0 \rightarrow W^{-1,q} for a q>3q>3 in the case when the coefficient function μ\mu has a jump across a C1C^1 interface and is continuous elsewhere. A counterexample shows that the C1C^1 condition cannot be relaxed in general. Finally, we draw some conclusions for corresponding parabolic operators.

Cite this article

Johannes Elschner, Joachim Rehberg, Gunther Schmidt, Optimal regularity for elliptic transmission problems including <em>C<sup>1</sup></em> interfaces. Interfaces Free Bound. 9 (2007), no. 2, pp. 233–252

DOI 10.4171/IFB/163