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.
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 |