JournalsifbVol. 9 , No. 2DOI 10.4171/ifb/163

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

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.