×
Balashova, G. S.

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.

MSC:

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

Keywords:

Sobolev problem of infinite order; multidimensional strip region; trace continuation
PDF BibTeX XML Cite
\textit{G. S. Balashova}, Math. Notes 62, No. 6, 688--696 (1997; Zbl 0914.46028); translation from Mat. Zametki 62, No. 6, 820--830 (1997)
Full Text: DOI

References:

[1] G. S. Balashova, ”Some continuation theorems in the infinite-order Sobolev space and nonhomogeneous boundary value problems,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],244, No. 6, 1294–1297 (1979).
[2] G. S. Balashova, ”On continuation theorems in spaces of infinitely differentiable functions,”Mat. Sb. [Math. USSR-Sb.],118 (160), No. 3, 371–385 (1982).
[3] G. S. Balashova, ”On continuation of infinitely differentiable functions,”Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],51, No. 6, 1292–1308 (1987). · Zbl 0643.26015
[4] G. S. Balashova, ”On continuation conditions for the trace and embeddings in Banach spaces of infinitely differentiable functions,”Mat. Sb. [Russian Acad. Sci. Sb. Math.],184, No. 1, 105–128 (1993). · Zbl 0834.46022
[5] G. S. Balashova, ”The continuation and embedding theorems for Sobolev spaces of infinite order,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],319, No. 2, 267–270 (1991). · Zbl 0798.46020
[6] Yu. A. Dubinskii, ”Traces of functions from Sobolev spaces of infinite order and nonhomogeneous problems for nonlinear equations,”Mat. Sb. [Math. USSR-Sb.],106 (148), No. 1, 66–84 (1978).
[7] S. Mandelbrojt,Séries adhérentes. Régularisation des suites. Applications, Paris (1952).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.