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.
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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. 233–252DOI 10.4171/IFB/163