Trace continuation in infinite-order Sobolev space on a multidimensional strip region. (English. Russian original) Zbl 0914.46028

Math. Notes 62, No. 6, 688-696 (1997); translation from Mat. Zametki 62, No. 6, 820-830 (1997).
Summary: In the Sobolev infinite-order space on a multidimensional strip region, we obtain conditions for the existence of a function that, together with all its derivatives, assumes prescribed values on the boundary. An example shows that the sufficient conditions for the trace continuation obtained in the present paper have a significant advantage over those obtained earlier. Furthermore, for spaces of some special type our conditions for trace continuation are both sufficient and necessary.


46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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