Sobolev functions whose inner trace at the boundary is zero |
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Authors: | David Swanson William P. Ziemer |
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Affiliation: | (1) Department of Mathematics, Indiana University, 47405 Bloomington, IN, USA |
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Abstract: | Let Ω⊂R n be an arbitrary open set. In this paper it is shown that if a Sobolev functionf∈W 1,p (Ω) possesses a zero trace (in the sense of Lebesgue points) on ϖΩ, thenf is weakly zero on ϖΩ in the sense thatf∈W 0 1,p (Ω). |
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