WIAS Preprint No. 1094, (2006)

Optimal regularity for elliptic transmission problems including $C^1$ interfaces



Authors

  • Elschner, Johannes
  • Rehberg, Joachim
  • Schmidt, Gunther

2010 Mathematics Subject Classification

  • 35B45 35B65 35D10 35J15 35Q40

Keywords

  • Partial differential equations, elliptic operators, nonsmooth domains, transmission problems, discontinuous coefficients

Abstract

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.

Appeared in

  • Interfaces Free Bound., 9 (2007) pp. 233--252.

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