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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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).

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

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

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1999 © Institut Mittag-Leffler


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.

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