Anisotropic Lizorkin–Triebel spaces with mixed norms — traces on smooth boundaries |
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Authors: | J Johnsen S Munch Hansen W Sickel |
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Institution: | 1. Department of Mathematical Sciences, Aalborg University, Aalborg, ?st, Denmark;2. Institute of Mathematics, Friedrich‐Schiller‐University Jena, Jena, Germany |
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Abstract: | This article deals with trace operators on anisotropic Lizorkin–Triebel spaces with mixed norms over cylindrical domains with smooth boundary. As a preparation we include a rather self‐contained exposition of Lizorkin–Triebel spaces on manifolds and extend these results to mixed‐norm Lizorkin–Triebel spaces on cylinders in Euclidean space. In addition Rychkov's universal extension operator for a half space is shown to be bounded with respect to the mixed norms, and a support preserving right‐inverse of the trace is given explicitly and proved to be continuous in the scale of mixed‐norm Lizorkin–Triebel spaces. As an application, the heat equation is considered in these spaces, and the necessary compatibility conditions on the data are deduced. |
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Keywords: | Trace operators mixed norms cylindrical domains parabolic boundary problems Primary: 46E35 Secondary: 35K20 |
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