Anisotropic Lizorkin-Triebel spaces with mixed norms traces on smooth boundaries

作者：Johnsen J^*; Hansen S Munch; Sickel W

来源：Mathematische Nachrichten, 2015, 288(11-12): 1327-1359.

DOI：10.1002/mana.201300313

• Trace operators
• mixed norms
• cylindrical domains
• parabolic boundary problems

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.

• 出版日期2015-8