Article PDF
Avoid common mistakes on your manuscript.
References
L. R. Volevich, “Local properties of solutions to quasielliptic systems,” Mat. Sb.,59, No. 3, 3–52 (1962).
G. V. Demidenko, “Integral operators determined by quasielliptic equations. I,” Sibirsk. Mat. Zh.34, No. 6, 52–67 (1993).
G. V. Demidenko, “On weighted Sobolev spaces and integral operators determined by quasielliptic equations,” Dokl. Akad. Nauk,334, No. 4, 420–423 (1994).
L. D. Kudryavtsev, “Embedding theorems for classes of functions determined in the whole space or in the half-space,” I: Mat. Sb.,69, No. 4, 616–639 (1966); II: Mat. Sb.,70, No. 1, 3–35 (1966).
L. D. Kudryavtsev and S. M. Nikol'skiî, “Spaces of differentiable functions in several variables and embedding theorems,” in: Contemporary Problems of Mathematics. Fundamental Trends [in Russian], VINITI, Moscow, 1988,26, pp. 5–157. (Itogi Nauki i Tekhniki.)
L. Nirenberg and H. F. Walker, “The null spaces of elliptic partial differential operators inR n,” J. Math. Anal. Appl.,42, No. 2, 271–301 (1973).
M. Cantor, “Elliptic operators and decomposition of tensor fields,” Bull. Amer. Math. Soc.,5, No. 3, 235–262 (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).
R. B. Lockhart, and R. C. McOwen, “Elliptic differential operators on noncompact manifolds,” Ann. Scuola Norm. Sup. Pisa Cl. Sci.,12, No. 3, 409–447 (1985).
G. V. Demidenko, “On properties of quasielliptic operators,” in: The Second Siberian Congress on Applied and Industrial Mathematics, Inst. Mat. (Novosibirsk), Novosibirsk, 1996, p. 92.
S. V. Uspenskii, “On representation of functions determined 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 pseudod-ifferential equations,” I: Sibirsk. Mat. Zh.,13, No. 3, 665–678 (1972); II: Sibirsk. Mat. Zh.13, No. 4, 903–909 (1972).
P. I. Lizorkin, “Generalized Liouville differentiation and the multiplier method in the theory of embeddings of classes of differentiable functions and its applications,” Trudy Mat. Inst. Steklov.,105, 89–167 (1969).
G. H. Hardy, D. E. Littlewood, and G. Pólya, Inequalities [Russian translation], Izdat. Inostr. Lit., Moscow (1948).
S. V. Uspenskiî, G. V. Demidenko, and V. G. Perepëlkin, Embedding Theorems and Applications to Differential Equations [in Russian], Nauka, Novosibirsk (1984).
G. V. Demidenko, “L p-theory of boundary value problems for Sobolev type equations,” in: Partial Differential Equations, Banach Center Publications, Warszawa, 1992,27, Part I, pp. 101–109.
Additional information
The research was financially supported by the Russian Foundation for Basic Research (Grant 95-01-01176).
Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 39, No. 5, pp. 1028–1037, September–October. 1998
Rights and permissions
About this article
Cite this article
Demidenko, G.V. On quasielliptic operators inR n † . Sib Math J 39, 884–893 (1998). https://doi.org/10.1007/BF02672910
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02672910