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.
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Original Russian Text Copyright © 2008 Demidenko G. V.
The author was supported by the Russian Foundation for Basic Research (Grant 07-01-00289) and the Siberian Division of the Russian Academy of Sciences (Grant No. 2.2).
In Memory of Sergeĭ L’vovich Sobolev.
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Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 5, pp. 1064–1076, September–October, 2008.
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Demidenko, G.V. Quasielliptic operators and Sobolev type equations. Sib Math J 49, 842–851 (2008). https://doi.org/10.1007/s11202-008-0083-z
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DOI: https://doi.org/10.1007/s11202-008-0083-z