Selšuk Journal of Applied Mathematics

 Selšuk Journal of
  Applied Mathematics

  Summer-Autumn, 2002
  Volume  3
  Number 2

Research Center of 
  Applied Mathematics

 SJAM Summer-Autumn 2002, Volume 3 - Number 2

On properties of a class of matrix differential operators in Rn*

Gennadii Demidenko

Sobolev Institute of Mathematics, SB RAS,
Pr. Koptyuga 4, 630090 Novosibirsk, Russia
   email : ;

Received: August 01, 2002

In the paper we consider a class of matrix quasi-elliptic operators in $R^n$. We establish isomorphic properties of these operators in special weighted Sobolev spaces $W^l_{p,\sigma}(R^n)$. From our results a theorem on isomorphism for the Navier-Stokes operator follows.


Key words
matrix quasi-elliptic operators, the Navier-Stokes operator, isomorphism, weighted Sobolev spaces.

2000 Mathematics Subject Classification : 35A30, 35J45, 35Q30
* The research was supported in part by the Russian Foundation for Basic Research  (No. 01-01-00609).

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