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Jan 01, 1993
Integral operators determined by quasielliptic equations. I
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References
26
[1]
S. V. Uspenskiî, ?On representation of functions defined by a certain class of hypoelliptic operators,? Trudy Mat. Inst. Steklov.,117, 292?299 (1972).
[2]
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).
[3]
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.
[4]
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.
[5]
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.
[6]
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).
[7]
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).
[8]
S. L. Sobolev, Some Applications of Functional Analysis to Mathematical Physics [in Russian], Izdat. Leningrad. Univ., Leningrad (1950).
[9]
O. K. Friedrichs, ?Symmetric positive linear differential equations,? Comm. Pure Appl. Math.,11, 333?418 (1958).
10.1002/cpa.3160110306
[10]
L. Nirenberg and H. F. Walker, ?The null spaces of elliptic partial differential operators in ? n ,? J. Math. Anal. Appl.,42, No. 2, 271?301 (1973).
10.1016/0022-247x(73)90138-8
[11]
M. Cantor, ?Spaces of functions with asymptotic conditions on ? n ,? Indiana Univ. Math. J.,24, No. 9, 897?902 (1975).
10.1512/iumj.1975.24.24072
[12]
M. Cantor, ?Boundary value problems for asymptotically homogeneous elliptic second-order operators,? J. Differential Equations,34, No. 1, 102?113 (1979).
10.1016/0022-0396(79)90020-2
[13]
R. C. McOwen, ?The behavior of the Laplacian on weighted Sobolev spaces,? Comm. Pure Appl. Math.,32, No. 6, 783?795 (1979).
10.1002/cpa.3160320604
[14]
R. C. McOwen, ?Boundary value problems for the Laplacian in an exterior domain,? Comm. Partial Differential Equations,6, No. 7, 783?798 (1981).
10.1080/0360530810882192
[15]
R. B. Lockhart, ?Fredholm properties of a class of elliptic operators on noncompact manifolds,? Duke Math. J.,48, No. 1, 289?312 (1981).
10.1215/s0012-7094-81-04817-1
[16]
Y. Choquet-Bruhat and D. Christodoulou, ?Elliptic systems inH s ,? spaces on manifolds which are Euclidean at infinity,? Acta Math.,146, No. 1, 2, 129?150 (1981).
10.1007/bf02392460
[17]
L. A. Bagirov and V. A. Kondrat'ev, ?On elliptic equations in ? n ,? Differentsial'nye Uravneniya,11, No. 3, 498?504 (1975).
[18]
L. A. Bagirov, ?A priori estimates, existence theorems, and the behavior at infinity of solutions to quasielliptic equations in ? n ,? Mat. Sb.,110, No. 4, 475?492 (1979).
[19]
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.
[20]
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).
[21]
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.
[22]
S. L. Sobolev, Selected Topics of the Theory of Function Spaces and Generalized Functions [in Russian], Nauka, Moscow (1989).
[23]
G. V. Demidenko,L p -Estimates for Solutions to Quasielliptic Equations in ? n ? [in Russian] [Preprint, No. 4], Inst. Mat. (Novosibirsk), Novosibirsk (1992).
[24]
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).
[25]
L. D. Kudryavtsev, ?Embedding theorems for functions defined on unbounded regions,? Dokl. Akad. Nauk SSSR,153, No. 3, 530?532 (1963).
[26]
H. Triebel, Interpolation Theory, Function Spaces, and Differential Operators [Russian translation], Mir, Moscow (1980).
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Details
- Published
- Jan 01, 1993
- Vol/Issue
- 34(6)
- Pages
- 1044-1058
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Cite This Article
G. V. Demidenko (1993). Integral operators determined by quasielliptic equations. I. Siberian Mathematical Journal, 34(6), 1044-1058. https://doi.org/10.1007/bf00973468
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