This is a preview of subscription content, log in via an institution to check access.
References
M. Yu. Vasil'chik, “On the traces of functions of the Sobolev space defined on a plane domain with non-Lipschitz boundary,” Dokl. Akad. Nauk SSSR,319, No. 2, 275–277 (1991).
M. Yu. Vasil'chik, “On necessary and sufficient conditions on the trace of a function of the Sobolev space on the boundary of a plane domain with non-Lipschitz boundary,” in: Studies on Mathematical Analysis and Riemannian Geometry. Vol. 21 [in Russian], Trudy Inst. Mat. (Novosibirsk), Nauka, Novosibirsk, 1992, pp. 5–29.
S. M. Nikol'skii, “Boundary properties of functions defined on domains with angular points. I–III,” Mat. Sb., I:40, No. 3, 303–318 (1956); II:43, No. 1, 127–144 (1957); III:45, No. 2, 181–194 (1958).
G. N. Yakovlev, “Boundary properties of functions of the classW (l) p on domains with angular points,” Dokl. Akad. Nauk SSSR,140, No. 1, 73–76 (1961).
G. N. Yakovlev, “On the traces of functions of the spaceW l p on piecewise smooth surfaces,” Mat. Sb.,74, No. 4, 526–543 (1967).
N. Aronszajn and P. Szeptycki, “Theory of Bessel potentials. IV. Potentials on subcartesian spaces with singularities of polyhedral type,” Ann. Inst. Fourier (Grenoble),25, No. 3–4, 27–69 (1975).
A. Jonsson, “Besov spaces on Lipschitz surfaces,” Dep. Math. Univ. Umea / Publ., No. 7, 1–12 (1986).
J. Marschall, “The trace of Sobolev-Slobodeckij spaces on Lipschitz domains,” Manuscripta Math.,58, No. 1–2, 47–65 (1987).
P. Grisvard, Elliptic Problems in Nonsmooth Domains, Pitman, Boston (1985).
G. N. Yakovlev, “The Dirichlet problem for domains with non-Lipschitz boundary,” Differentsial'nye Uravneniya,1, No. 8, 1085–1098 (1965).
V. G. Maz'ya, “On functions with finite Dirichlet integral in a domain with a cusp point on the boundary,” Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI),126, 117–137 (1983).
V. G. Maz'ya and S. V. Poborchii, “The traces of functions of Sobolev spaces on the boundary of a domain with a cusp,” in: Contemporary Problems of Geometry and Analysis. Vol. 14 [in Russian], Trudy Inst. Mat. (Novosibirsk), Nauka, Novosibirsk, 1989, pp. 182–208.
M. Yu. Vasil'chik, “On the traces of functions of the Sobolev spacesW 1 p defined on domains with non-Lipschitz boundary,” in: Contemporary Problems of Geometry and Analysis. Vol. 14 [in Russian], Trudy Inst. Mat. (Novosibirsk), Nauka, Novosibirsk, 1989, pp. 9–45.
V. G. Maz'ya and S. V. Poborchii, “On the traces of functions with summable gradient in a domain with a cusp on the boundary,” Mat. Zametki,45, No. 1, 57–65 (1989).
O. V. Besov, V. P. Il'in, and C. M. Nikol'skii, Integral Representations and Embedding Theorems [in Russian], Nauka, Moscow (1975).
V. I. Burenkov, “On additivity of the classesW (r) p (ω),” Trudy Mat. Inst. Steklov,89, 31–54 (1967).
Author information
Authors and Affiliations
Additional information
Translated fromSibirskii Matematicheskii Zhurnal, Vol. 36, No. 4, pp. 787–804, July–August, 1995.
Rights and permissions
About this article
Cite this article
Vasil'chik, M.Y. Boundary properties of functions of the Sobolev space defined in a planar domain with angular points. Sib Math J 36, 677–693 (1995). https://doi.org/10.1007/BF02107325
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02107325