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 Mat. Sb. (N.S.), 1978, Volume 106(148), Number 1(5), Pages 66–84 (Mi msb2553)

Traces of functions from Sobolev spaces of infinite order and inhomogeneous problems for nonlinear equations

Yu. A. Dubinskii

Abstract: The paper is devoted to the theory of “traces” in the spaces
$$W^\infty\{a_\alpha,p_\alpha\}(G)=\{u(x)\in C^\infty(G):\quad\sum_{|\alpha|=0}^{\infty}a_\alpha\|D^\alpha u\|_{p_\alpha}^{p_\alpha}<\infty\}$$
and to the inhomogeneous Dirichlet problem for elliptic equations of infinite order. A trace criterion is established, simple sufficient trace conditions are adduced, and the correctness of the indicated Dirichlet problem is proved on the basis of the results obtained.
Bibliography: 6 titles.

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English version:
Mathematics of the USSR-Sbornik, 1978, 34:5, 627–644

Bibliographic databases:

UDC: 517.9
MSC: 46E35, 35J60

Citation: Yu. A. Dubinskii, “Traces of functions from Sobolev spaces of infinite order and inhomogeneous problems for nonlinear equations”, Mat. Sb. (N.S.), 106(148):1(5) (1978), 66–84; Math. USSR-Sb., 34:5 (1978), 627–644

Citation in format AMSBIB
\Bibitem{Dub78} \by Yu.~A.~Dubinskii \paper Traces of functions from Sobolev spaces of infinite order and inhomogeneous problems for nonlinear equations \jour Mat. Sb. (N.S.) \yr 1978 \vol 106(148) \issue 1(5) \pages 66--84 \mathnet{http://mi.mathnet.ru/msb2553} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=493304} \zmath{https://zbmath.org/?q=an:0391.35027|0414.35028} \transl \jour Math. USSR-Sb. \yr 1978 \vol 34 \issue 5 \pages 627--644 \crossref{https://doi.org/10.1070/SM1978v034n05ABEH001334} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. G. S. Balashova, “On extension theorems in spaces of infinitely differentiable functions”, Math. USSR-Sb., 46:3 (1983), 375–389
2. Kobilov A., “Non-Triviality of Some Spaces of Infinitely Differentiable Functions in Corner Domains and the Solvability of Non-Linear Elliptic-Equations”, 266, no. 5, 1982, 1040–1044
3. G. S. Balashova, “On the extension of infinitely differentiable functions”, Math. USSR-Izv., 31:3 (1988), 603–620
4. Ha Huy Bang, “On imbedding theorems in Sobolev spaces of infinite order”, Math. USSR-Sb., 64:1 (1989), 115–127
5. Yu. A. Dubinskii, “Sobolev spaces of infinite order”, Russian Math. Surveys, 46:6 (1991), 107–147
6. G. S. Balashova, “Trace continuation in infinite-order Sobolev space on a multidimensional strip region”, Math. Notes, 62:6 (1997), 688–696
7. Balashova G., “On the Sobolev Spaces of Infinite Order”, Dokl. Akad. Nauk, 353:2 (1997), 151–152
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