1 results
Search Results
Now showing 1 - 1 of 1
- ItemOptimal regularity for elliptic transmission problems including C1 interfaces(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Elschner, Johannes; Rehberg, Joachim; Schmidt, GuntherWe 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.