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

Johannes Elschner | Zendy; Joachim Rehberg | Zendy; G. Schmidt | Zendy

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

Author(s) -

Johannes Elschner,

Joachim Rehberg,

G. Schmidt

Publication year - 2007

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/163

Subject(s) - nabla symbol , counterexample , jump , mathematics , function (biology) , transmission (telecommunications) , elliptic operator , elliptic function , pure mathematics , mathematical analysis , discrete mathematics , physics , computer science , quantum mechanics , telecommunications , evolutionary biology , omega , biology

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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