Quasielliptic Operators and Equations Not Solvable with Respect to the Higher Order Derivative
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We consider a class of quasielliptic operators in Rn and establish the isomorphism property in special weighted Sobolev spaces. In more general weighted spaces, we obtain the unique solvability conditions for quasielliptic equations and prove estimates for solutions. Based on the obtained results, we study the solvability of the initial problem for equations that are not solvable with respect to the higher order derivative.
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- 4.L. A. Bagirov and V. A. Kondratiev, “Elliptic equations in R n,” Differ. Equations 11, 375–379 (1975).Google Scholar
- 6.R. C. McOwen, On elliptic operators in R n,” Commun. Partial Differ. Equations 5, No. 9, 913–933 (1980).Google Scholar
- 14.G. V. Demidenko, “On weighted Sobolev spaces and integral operators determined by quasielliptic equations,” Russ. Acad. Sci., Dokl., Math. 49, No. 1, 113–118 (1994).Google Scholar
- 15.L. D. Kudryavtsev, “Imbedding theorems for classes of functions defined on the entire space or on a half space. I. II,” Am. Math. Soc., Transl., II. Ser. 74, 199–225; 227–260 (1968).Google Scholar
- 17.M. Cantor, “Elliptic operators and the decomposition of tensor fields,” Bull. Am. Math. Soc., New Ser. 5, No. 3, 235–262 (1981).Google Scholar
- 18.S. L. Sobolev, Selected Works. I Springer, New York (2006).Google Scholar
- 20.S. V. Uspenskii, “The representation of functions defined by a certain class of hypoelliptic operators,” Proc. Steklov Inst. Math. 117, 343–352 (1972).Google Scholar
- 21.P. I. Lizorkin, “Generalized Liouville differentiation and the multiplier method in the theory of imbeddings of classes of differentiable functions,” Proc. Steklov Inst. Math. 105, 105–202 (1969).Google Scholar
- 22.G. H. Hardy, J. E. Littlewood, and G. Pólia, Inequalities, Cambridge Univ. Press, Cambridge (1934).Google Scholar