Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A proof of the trace theorem of Sobolev spaces on Lipschitz domains

Author: Zhonghai Ding
Journal: Proc. Amer. Math. Soc. 124 (1996), 591-600
MSC (1991): Primary 46E35
MathSciNet review: 1301021
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A complete proof of the trace theorem of Sobolev spaces on Lipschitz domains has not appeared in the literature yet. The purpose of this paper is to give a complete proof of the trace theorem of Sobolev spaces on Lipschitz domains by taking advantage of the intrinsic norm on $H^{s}(\partial \Omega )$. It is proved that the trace operator is a linear bounded operator from $H^{s}(\Omega )$ to $H^{s-\frac {1}{2}}(\partial \Omega )$ for $\frac {1}{2}<s<\frac {3}{2}$.

References [Enhancements On Off] (What's this?)

  • Robert A. Adams, Sobolev spaces, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Pure and Applied Mathematics, Vol. 65. MR 0450957
  • Martin Costabel, Boundary integral operators on Lipschitz domains: elementary results, SIAM J. Math. Anal. 19 (1988), no. 3, 613–626. MR 937473, DOI
  • Z. Ding and J. Zhou, Constrained LQR problems governed by the potential equation on Lipschitz domain with point observations, J. Math. Pures Appl. 74 (1995), 317–344.
  • Emilio Gagliardo, Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in $n$ variabili, Rend. Sem. Mat. Univ. Padova 27 (1957), 284–305 (Italian). MR 102739
  • P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics, vol. 24, Pitman (Advanced Publishing Program), Boston, MA, 1985. MR 775683
  • David S. Jerison and Carlos E. Kenig, Boundary value problems on Lipschitz domains, Studies in partial differential equations, MAA Stud. Math., vol. 23, Math. Assoc. America, Washington, DC, 1982, pp. 1–68. MR 716504
  • Carlos E. Kenig, Recent progress on boundary value problems on Lipschitz domains, Pseudodifferential operators and applications (Notre Dame, Ind., 1984) Proc. Sympos. Pure Math., vol. 43, Amer. Math. Soc., Providence, RI, 1985, pp. 175–205. MR 812291, DOI
  • J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications. Vol. I, Springer-Verlag, New York-Heidelberg, 1972. Translated from the French by P. Kenneth; Die Grundlehren der mathematischen Wissenschaften, Band 181. MR 0350177
  • Gregory Verchota, Layer potentials and regularity for the Dirichlet problem for Laplace’s equation in Lipschitz domains, J. Funct. Anal. 59 (1984), no. 3, 572–611. MR 769382, DOI

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46E35

Retrieve articles in all journals with MSC (1991): 46E35

Additional Information

Zhonghai Ding
Affiliation: Department of Mathematics Texas A&M University College Station, Texas 77843
Address at time of publication: Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, Nevada 89154

Keywords: Sobolev spaces, Lipschitz domains, trace theorem
Received by editor(s): September 15, 1994
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society