Optimal regularity for elliptic transmission problems including C 1 interfaces

Abstract

We prove an optimal regularity result for elliptic operators -∇ · ∇: W01,q→ W-1,qfor a q > 3 in the case when the coefficient function μ has a jump across a C 1 interface and is continuous elsewhere. A counterexample shows that the C1 condition cannot be relaxed in general. Finally, we draw some conclusions for corresponding parabolic operators. © European Mathematical Society 2007.