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Sib. J. Pure and Appl. Math., 2016, Volume 16, Issue 3, Pages 15–26 (Mi vngu407)  

Quasielliptic operators and equations not solvable with respect to the highest order derivative

G. V. Demidenkoab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University

Abstract: We consider a class of quasielliptic operators in the whole space. Isomorphism properties in special weighted Sobolev spaces are established. We obtain conditions for unique solvability of the quasielliptic equations and estimates for their solutions in more general weighted spaces. Using the established results, we study solvability of the initial value problem for equations not solvable with respect to the highest order derivative.

Keywords: quasielliptic operators, weighted Sobolev spaces, isomorphism, Sobolev type equations.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0314-2015-0011


DOI: https://doi.org/10.17377/PAM.2016.16.302

Full text: PDF file (213 kB)
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English version:
Journal of Mathematical Sciences, 2018, 230:1, 25–35

Document Type: Article
UDC: 517.953 + 517.983
Received: 07.05.2016

Citation: G. V. Demidenko, “Quasielliptic operators and equations not solvable with respect to the highest order derivative”, Sib. J. Pure and Appl. Math., 16:3 (2016), 15–26; J. Math. Sci., 230:1 (2018), 25–35

Citation in format AMSBIB
\Bibitem{Dem16}
\by G.~V.~Demidenko
\paper Quasielliptic operators and equations not solvable with respect to the highest order derivative
\jour Sib. J. Pure and Appl. Math.
\yr 2016
\vol 16
\issue 3
\pages 15--26
\mathnet{http://mi.mathnet.ru/vngu407}
\crossref{https://doi.org/10.17377/PAM.2016.16.302}
\transl
\jour J. Math. Sci.
\yr 2018
\vol 230
\issue 1
\pages 25--35
\crossref{https://doi.org/10.1007/s10958-018-3723-2}


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