Abstract
Let Ω⊂Rn be an arbitrary open set. In this paper it is shown that if a Sobolev function f∈W1, 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 f∈W ${}_{0}^{1,p}$ (Ω).
Citation
David Swanson. William P. Ziemer. "Sobolev functions whose inner trace at the boundary is zero." Ark. Mat. 37 (2) 373 - 380, October 1999. https://doi.org/10.1007/BF02412221
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