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

Please always quote using this URN:urn:nbn:de:0296-matheon-4604
  • 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.

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Metadaten
Author:Johannes Elschner, Joachim Rehberg, Gunther Schmidt
URN:urn:nbn:de:0296-matheon-4604
Referee:Alexander Mielke
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2008/02/19
Release Date:2008/01/02
Tag:
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B45 A priori estimates
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B65 Smoothness and regularity of solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J15 Second-order elliptic equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q40 PDEs in connection with quantum mechanics
Preprint Number:443
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