Literature Cited
S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics [in Russian], Izdat. Sibirsk. Otdel. Akad. Nauk SSSR (1962).
S. M. Nikol'skii, “Properties of certain classes of several variables on differentiable manifolds,” Matem. Sb.,33, (75), No. 2, 261–326 (1963).
L. N. Slobodetskii, “Generalized Sobolev spaces of fractional order and their applications to boundary value problems for partial differential equations,” Uch. Zap. Lenin. Gos. Univ. Fiz.-Mat. Fak.,197, 54–112 (1958).
E. Gagliardo, “Caratterizazioni delle trace sulla frontiera relative ad alcune classi di funzioni in n variabili,” Rend. Sem. Mat. Padova,27, 284–305 (1957).
O. V. Besov, “Investigation of a family of function spaces in connection with imbedding and extension theorems,” Trudy Mat. Inst. Steklov,60, 42–81 (1961).
V. P. Il'in, “On certain properties of classes of differentiable functions defined in domains,” Trudy Mat. Inst. Steklov,84, 93–143 (1965).
A. P. Il'in and V. A. Solonnikov, “On certain properties of differentiable functions of several variables,” Dokl. Akad. Nauk SSSR,136, No. 3, 538–541 (1961).
S. M. Nikol'skii, “On the stability of the boundary values of a differentiable function of several variables,” Matem. Sb.,61, (103), No. 2, 224–242 (1963).
S. V. Uspenskii, “On embedding theorems in domains,” Sibirsk. Matem. Zh.,7, No. 3, 650–663 (1966).
Ya. S. Bugrov, “Embedding theorems for certain function classes,” Trudy Mat. Inst. Steklov,77, 45–64 (1965).
Ya. S. Bugrov, “Boundary properties of functions of the class H rp on domains having corner points,” Sibirsk. Matem. Zh.,5, No. 5, 1007–1026 (1964).
M. D. Ramazanov, “Theorems on the traces and extensions of functions from surfaces,” Dokl. Akad. Nauk SSSR,190, No. 4, 784–787 (1970).
M. D. Ramazanov, “Restrictions des fonctions des w k2 espaces aux surfaces lisses,” C. R. Acad. Sci. Paris,269, No. 25, 1202–1204 (1969).
O. v. Besov, “On the extension of functions from L lp and W lp ,” Trudy Mat. Inst. Steklov,89, 5–17 (1967).
V. P. Il'in, “Integral representations of differentiable functions and their application to problems on the extension of the classes W lp ,” Sibirsk. Matem. Zh.,8, No. 3, 573–586 (1967).
S. V. Uspenskii, “On the mixed derivatives of functions, summable with a weight,” Differentsial Uravnen.,3, No. 1, 139–154 (1967).
S. V. Uspenskii, “On the trace of functions belonging to the class of S. M. Nikol'skii,” Sibirsk. Matem. Zh.,6, No. 3, 574–580 (1965).
S. V. Uspenskii, “Embedding and extension theorems. II,” Sibirsk. Matem. Zh.,7, No. 2, 409–418 (1966)
L. Hörmander, Linear Partial Differential Operators, Springer-Verlag, Berlin-Göttingen-Heidelberg (1963).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 13, No. 2, pp. 429–451, March–April, 1972.
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Uspenskii, S.V. On the traces, on smooth surfaces, of functions of the Sobolev class\(W_p^{l_1 \cdot \cdot \cdot l_n } \) . Sib Math J 13, 298–313 (1972). https://doi.org/10.1007/BF00971618
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DOI: https://doi.org/10.1007/BF00971618