TY - GEN A1 - Elschner, Johannes A1 - Rehberg, Joachim A1 - Schmidt, Gunther T1 - Optimal regularity for elliptic transmission problems including $C^1$ interfaces N2 - We prove an optimal regularity result for elliptic operators $-\nabla \cdot \mu \nabla:W^1,q_0 \rightarrow W^-1,q$ for a $q>3$ in the case when the coefficient function $\mu$ has a jump across a $C^1$ interface and is continuous elsewhere. A counterexample shows that the $C^1$ condition cannot be relaxed in general. Finally, we draw some conclusions for corresponding parabolic operators. KW - Partial differential equations KW - elliptic operators KW - nonsmooth domains KW - transmission problems KW - discontinuous coefficients Y1 - 2008 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/460 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-4604 ER -