In this paper, a trace theorem and several lemmas for a class of anisotropic Sobolev spaces are given. These results are used to study the initial boundary value problem for symmetric hyperbolic systems with characteristic boundary of constant multiplicity. Especially, the trace theorem is needed for showing the necessity of the compatibility condition for the existence of solution to the characteristic mixed problem mentioned above.
Yasushi Shizuta. Yumi Tanaka. "Trace theorem in a class of anisotropic Sobolev spaces." Proc. Japan Acad. Ser. A Math. Sci. 76 (3) 27 - 30, March 2000. https://doi.org/10.3792/pjaa.76.27