Abstract
We consider matrix quasielliptic operators on the whole space. Under the quasihomogeneity condition for symbols, we establish the isomorphism theorem for these operators in the special scales of Sobolev spaces. In particular, this result implies a series of available isomorphism theorems for elliptic operators and theorems about the unique solvability of the initial value problem for a broad class of systems of Sobolev type.
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To Yu. G. Reshetnyak on his 80th birthday.
Original Russian Text Copyright © 2009 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. 85).
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Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 5, pp. 1060–1069, September–October, 2009.
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Demidenko, G.V. Quasielliptic operators and Sobolev type equations. II. Sib Math J 50, 838–845 (2009). https://doi.org/10.1007/s11202-009-0094-4
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DOI: https://doi.org/10.1007/s11202-009-0094-4