Optimal regularity for elliptic transmission problems including 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

Abstract

We prove an optimal regularity result for elliptic operators for a in the case when the coefficient function has a jump across a interface and is continuous elsewhere. A counterexample shows that the 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 interfaces. Interfaces Free Bound. 9 (2007), no. 2, pp. 233–252

DOI 10.4171/IFB/163