Optimal regularity for elliptic transmission problems including C1 interfaces

Abstract

We prove an optimal regularity result for elliptic operators −nablacdotmunabla:W1,q0rightarrowW−1,q for a q>3 in the case when the coefficient function mu has a jump across a C1 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.