This is a preview of subscription content, log in via an institution to check access.
References
S. V. Uspenskiî, “On representation of functions defined by a certain class of hypoelliptic operators,” Trudy Mat. Inst. Steklov.,117, 292–299 (1972).
S. V. Uspenskiî, “On differential properties at infinity of solutions to a certain class of pseudodifferential equations,” I: Sibirsk. Mat. Zh.,13, No. 3, 665–678 (1972); II: Sibirsk. Mat. Zh.,13, No. 4, 903–909 (1972).
S. V. Uspenskiî and B. N. Chistyakov, “On exit to a polynomial of solutions to a certain class of pseudodifferential equations as |x|→∞,” in: The Theory of Cubature Formulas and Applications of Functional Analysis to Equations of Mathematical Physics [in Russian], Inst. Mat. (Novosibirsk), Novosibirsk, No. 1, 1979, pp. 119–135.
P. S. Filatov, “Uniform estimates at infinity for solutions to a certain class of quasielliptic equations,” in: Partial Differential Equations [in Russian], Inst. Mat. (Novosibirsk), Novosibirsk, No. 2, 1979, pp. 124–136.
G. A. Shrnyrëv, “On exit to a polynomial of solutions to a certain class of equations of quasielliptic type as |x|→∞,” in: Embedding Theorems and Their Applications to Problems of Mathematical Physics [in Russian], Inst. Mat. (Novosibirsk), Novosibirsk, No. 1, 1983, pp. 134–147.
G. A. Shmyrëv and B. N. Chistyakov, On Properties at Infinity of Functions Defined by a Certain Family of Pseudodifferential Operators [in Russian], [Preprint, No. 25], Inst. Mat. (Novosibirsk), Novosibirsk (1988).
P. S. Filatov, “Orthogonality conditions and the behavior at infinity of solutions to a certain class of quasielliptic equations,” Sibirsk. Mat. Zh.,29, No. 5, 226–235 (1988).
S. L. Sobolev, Some Applications of Functional Analysis to Mathematical Physics [in Russian], Izdat. Leningrad. Univ., Leningrad (1950).
O. K. Friedrichs, “Symmetric positive linear differential equations,” Comm. Pure Appl. Math.,11, 333–418 (1958).
L. Nirenberg and H. F. Walker, “The null spaces of elliptic partial differential operators in ℝn,” J. Math. Anal. Appl.,42, No. 2, 271–301 (1973).
M. Cantor, “Spaces of functions with asymptotic conditions on ℝn,” Indiana Univ. Math. J.,24, No. 9, 897–902 (1975).
M. Cantor, “Boundary value problems for asymptotically homogeneous elliptic second-order operators,” J. Differential Equations,34, No. 1, 102–113 (1979).
R. C. McOwen, “The behavior of the Laplacian on weighted Sobolev spaces,” Comm. Pure Appl. Math.,32, No. 6, 783–795 (1979).
R. C. McOwen, “Boundary value problems for the Laplacian in an exterior domain,” Comm. Partial Differential Equations,6, No. 7, 783–798 (1981).
R. B. Lockhart, “Fredholm properties of a class of elliptic operators on noncompact manifolds,” Duke Math. J.,48, No. 1, 289–312 (1981).
Y. Choquet-Bruhat and D. Christodoulou, “Elliptic systems inH s ,σ spaces on manifolds which are Euclidean at infinity,” Acta Math.,146, No. 1, 2, 129–150 (1981).
L. A. Bagirov and V. A. Kondrat'ev, “On elliptic equations in ℝ n ,” Differentsial'nye Uravneniya,11, No. 3, 498–504 (1975).
L. A. Bagirov, “A priori estimates, existence theorems, and the behavior at infinity of solutions to quasielliptic equations in ℝ n ,” Mat. Sb.,110, No. 4, 475–492 (1979).
G. V. Demidenko, “On solvability conditions for mixed problems to a certain class of equations of Sobolev type,” in: Boundary Value Problems for Partial Differential Equations [in Russian], Inst. Mat. (Novosibirsk), Novosibirsk, 1984, pp. 23–54.
G. V. Demidenko, “On correct solvability of boundary value problems for quasielliptic equations in a half-space,” Sibirsk. Mat. Zh.,29, No. 4, 54–67 (1988).
O. V. Besov, V. P. Il'in, L. D. Kudryavtsev, P. I. Lizorkin, and S. M. Nikol'skiî, “Embedding theory for differentiable functions in several variables,” in: Partial Differential Equations [in Russian], Nauka, Moscow, 1970, pp. 38–63.
S. L. Sobolev, Selected Topics of the Theory of Function Spaces and Generalized Functions [in Russian], Nauka, Moscow (1989).
G. V. Demidenko,L p -Estimates for Solutions to Quasielliptic Equations in ℝ n ” [in Russian] [Preprint, No. 4], Inst. Mat. (Novosibirsk), Novosibirsk (1992).
P. I. Lizorkin, “Generalized Liouville differentiation and the multiplier method in embedding theory for classes of differentiable functions,” Trudy Mat. Inst. Steklov.,105, 89–167 (1969).
L. D. Kudryavtsev, “Embedding theorems for functions defined on unbounded regions,” Dokl. Akad. Nauk SSSR,153, No. 3, 530–532 (1963).
H. Triebel, Interpolation Theory, Function Spaces, and Differential Operators [Russian translation], Mir, Moscow (1980).
Additional information
Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 6, pp. 52–67, November–December, 1993.
Translated by G. V. Dyatlov
Rights and permissions
About this article
Cite this article
Demidenko, G.V. Integral operators determined by quasielliptic equations. I. Sib Math J 34, 1044–1058 (1993). https://doi.org/10.1007/BF00973468
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00973468