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Sibirsk. Mat. Zh., 2008, Volume 49, Number 5, Pages 1064–1076 (Mi smj1903)  

This article is cited in 6 scientific papers (total in 6 papers)

Quasielliptic operators and Sobolev type equations

G. V. Demidenko

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We consider a class of matrix quasielliptic operators on the $n$-dimensional space. For these operators, we establish the isomorphism properties in some special scales of weighted Sobolev spaces. Basing on these properties, we prove the unique solvability of the initial value problem for a class of Sobolev type equations.

Keywords: quasielliptic operator, weighted Sobolev space, isomorphism, Sobolev type equations.

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English version:
Siberian Mathematical Journal, 2008, 49:5, 842–851

Bibliographic databases:

UDC: 517.953+517.983
Received: 10.06.2008

Citation: G. V. Demidenko, “Quasielliptic operators and Sobolev type equations”, Sibirsk. Mat. Zh., 49:5 (2008), 1064–1076; Siberian Math. J., 49:5 (2008), 842–851

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. V. Demidenko, “Quasielliptic operators and Sobolev type equations. II”, Siberian Math. J., 50:5 (2009), 838–845  mathnet  crossref  mathscinet  isi  elib  elib
    2. Demidenko G.V., “Matrix quasi-elliptic operators in $\mathbb R^n$”, Dokl. Math., 81:2 (2010), 244–247  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. B. E. Kanguzhin, N. E. Tokmagambetov, “Resolvents of well-posed problems for finite-rank perturbations of the polyharmonic operator in a punctured domain”, Siberian Math. J., 57:2 (2016), 265–273  mathnet  crossref  crossref  mathscinet  isi  elib
    4. A. G. Tumanyan, “On Noethericity and index of differential operators in anisotropic weighted Sobolev spaces”, Uch. zapiski EGU, ser. Fizika i Matematika, 2016, no. 3, 63–69  mathnet
    5. G. V. Demidenko, “Quasielliptic operators and equations not solvable with respect to the highest order derivative”, J. Math. Sci., 230:1 (2018), 25–35  mathnet  crossref  crossref
    6. A. L. Kazakov, Sv. S. Orlov, S. S. Orlov, “Construction and study of exact solutions to a nonlinear heat equation”, Siberian Math. J., 59:3 (2018), 427–441  mathnet  crossref  crossref  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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