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

This article is cited in 7 scientific papers (total in 7 papers)

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.

Full text: PDF file (842 kB)
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English version:
Mathematics of the USSR-Sbornik, 1978, 34:5, 627–644

Bibliographic databases:

UDC: 517.9
MSC: 46E35, 35J60
Received: 06.07.1977

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  mathnet  crossref  mathscinet  zmath
    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  mathscinet  zmath  isi
    3. G. S. Balashova, “On the extension of infinitely differentiable functions”, Math. USSR-Izv., 31:3 (1988), 603–620  mathnet  crossref  mathscinet  zmath
    4. Ha Huy Bang, “On imbedding theorems in Sobolev spaces of infinite order”, Math. USSR-Sb., 64:1 (1989), 115–127  mathnet  crossref  mathscinet  zmath
    5. Yu. A. Dubinskii, “Sobolev spaces of infinite order”, Russian Math. Surveys, 46:6 (1991), 107–147  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. G. S. Balashova, “Trace continuation in infinite-order Sobolev space on a multidimensional strip region”, Math. Notes, 62:6 (1997), 688–696  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Balashova G., “On the Sobolev Spaces of Infinite Order”, Dokl. Akad. Nauk, 353:2 (1997), 151–152  mathnet  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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