Optimal regularity for elliptic transmission problems including $C^1$ interfaces
- Elschner, Johannes
- Rehberg, Joachim
- Schmidt, Gunther
2010 Mathematics Subject Classification
- 35B45 35B65 35D10 35J15 35Q40
- Partial differential equations, elliptic operators, nonsmooth domains, transmission problems, discontinuous coefficients
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.
- Interfaces Free Bound., 9 (2007) pp. 233--252.