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arXiv · 1608.04575

Anisotropic Lizorkin--Triebel Spaces with Mixed Norms --- Traces on Smooth Boundaries

Jon Johnsen·Sabrina Munch Hansen·Winfried Sickel
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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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Jon Johnsen, Sabrina Munch Hansen, Winfried Sickel. 2016-08-16. Anisotropic Lizorkin--Triebel Spaces with Mixed Norms --- Traces on Smooth Boundaries. https://doi.org/10.1002/mana.201300313

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