Sobolev functions whose inner trace at the boundary is zero
Let Ω⊂Rn be an arbitrary open set. In this paper it is shown that if a Sobolev functionf∈W1,p(Ω) possesses a zero trace (in the sense of Lebesgue points) on ϖΩ, thenf is weakly zero on ϖΩ in the sense thatf∈W01,p(Ω).