Geodesic
Optimal regularity for elliptic transmission problems including $C^1$ interfaces
Johannes Elschner1 ; Joachim Rehberg1 ; Gunther Schmidt1
1Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, Germany
Interfaces and free boundaries, Tome 9 (2007) no. 2, pp. 233-252

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DOI

We prove an optimal regularity result for elliptic operators −∇⋅μ∇:W01,q​→W−1,q for a q>3 in the case when the coefficient function μ 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.
DOI : 10.4171/ifb/163
Classification : 35-XX, 65-XX, 76-XX, 92-XX

Johannes Elschner  1   ; Joachim Rehberg  1   ; Gunther Schmidt  1

1 Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, Germany 
Johannes Elschner; Joachim Rehberg; Gunther Schmidt. Optimal regularity for elliptic transmission problems including $C^1$ interfaces. Interfaces and free boundaries, Tome 9 (2007) no. 2, pp. 233-252. doi: 10.4171/ifb/163
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     title = {Optimal regularity for elliptic transmission problems including $C^1$ interfaces},
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     pages = {233--252},
     year = {2007},
     volume = {9},
     number = {2},
     doi = {10.4171/ifb/163},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/163/}
}
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