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JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive

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

This article is cited in 14 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.

UDC: 517.953+517.983

Received: 10.06.2008


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

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© Steklov Math. Inst. of RAS, 2025