Search results for "Trace map"

The best constant for the Sobolev trace embedding from into

2004

Abstract In this paper we study the best constant, λ 1 ( Ω ) for the trace map from W 1 , 1 ( Ω ) into L 1 ( ∂ Ω ) . We show that this constant is attained in BV ( Ω ) when λ 1 ( Ω ) 1 . Moreover, we prove that this constant can be obtained as limit when p ↘ 1 of the best constant of W 1 , p ( Ω ) ↪ L p ( ∂ Ω ) . To perform the proofs we will look at Neumann problems involving the 1-Laplacian, Δ 1 ( u ) = div ( Du / | Du | ) .