Arkiv för Matematik

  • Ark. Mat.
  • Volume 37, Number 2 (1999), 373-380.

Sobolev functions whose inner trace at the boundary is zero

David Swanson and William P. Ziemer

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Abstract

Let Ω⊂Rn be an arbitrary open set. In this paper it is shown that if a Sobolev function fW1, p(Ω) possesses a zero trace (in the sense of Lebesgue points) on ϖΩ, then f is weakly zero on ϖΩ in the sense that fW ${}_{0}^{1,p}$ (Ω).

Article information

Source
Ark. Mat., Volume 37, Number 2 (1999), 373-380.

Dates
Received: 2 December 1997
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898641

Digital Object Identifier
doi:10.1007/BF02412221

Mathematical Reviews number (MathSciNet)
MR1714762

Zentralblatt MATH identifier
1021.46027

Rights
1999 © Institut Mittag-Leffler

Citation

Swanson, David; Ziemer, William P. Sobolev functions whose inner trace at the boundary is zero. Ark. Mat. 37 (1999), no. 2, 373--380. doi:10.1007/BF02412221. https://projecteuclid.org/euclid.afm/1485898641


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References

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