Abstract
In this paper we give some well-known trace theorems for Sobolev-Slobodeckij spaces under minimal regularity assumptions on the domain.
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References
Yu A. Brudnyi/P.A. Shvartsman, A Linear Extension Operator for a Space of Smooth Functions Defined on a Closed Subset ofR n, Soviet Math. Dokl. 31 (1985), 48–51
L.I. Hedberg/Th. Wolff, Thin Sets in Nonlinear Potential Theory, Ann. Inst. Fourier 33,4 (1983), 161–187
A. Jonsson, The Trace of the Zygmund Class ^k(R n) to Closed Sets and Interpolating Polynomials, J. Approx. Theory 44 (1985), 1–13
A. Jonsson/H. Wallin, Function Spaces on Subsets ofR n, Math. Reports 2/1 (1984)
A. Jonsson/H. Wallin, A Whitney Extension Theorem in Lp and Besov Spaces, Ann. Inst. Fourier 28,1 (1978), 139–192
A. Kufner/O. John/S. Fucik, Function Spaces, Noordhoff International Publishing, Leyden 1977
J. Necas, Les Méthodes Directes en Théorie des Equations Elliptiques Academia, Prague 1967
E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press 1970
H. Triebel, Interpolation Theory, Function Spaces and Differential Operators, North-Holland, Amsterdam-New York-Oxford 1978
H. Whitney, Functions Differentiable on the Boundary of Regions, Ann. Math. 35 (1934), 482–485
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Marschall, J. The trace of Sobolev-Slobodeckij spaces on Lipschitz domains. Manuscripta Math 58, 47–65 (1987). https://doi.org/10.1007/BF01169082
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DOI: https://doi.org/10.1007/BF01169082