6533b7d3fe1ef96bd126092f
RESEARCH PRODUCT
The best constant for the Sobolev trace embedding from into
José M. MazónFuensanta AndreuJulio D. Rossisubject
CombinatoricsSobolev spaceTrace (linear algebra)Applied MathematicsMathematical analysisNeumann boundary conditionEmbeddingTrace mapLimit (mathematics)Constant (mathematics)Laplace operatorAnalysisMathematicsdescription
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 | ) .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2004-12-01 | Nonlinear Analysis: Theory, Methods & Applications |