Browsing by Author "Andreu, F"

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    The best constant for the Sobolev trace embedding from W1,1 (Ω) into L1 (partial derivativeΩ)
    (2004) Andreu, F; Mazón, JM; Rossi, JD
    In this paper we study the best constant, lambda1 (Omega) for the trace map from W-1,W-1 (Omega) into L-1 (partial derivativeOmega). We show that this constant is attained in BV (Omega) when lambda(1) (Omega) < 1. Moreover, we prove that this constant can be obtained as limit when p SE arrow 1 of the best constant of W-1,W-p (Omega) -->. L-p (partial derivativeOmega). To perform the proofs we will look at Neumann problems involving the 1-Laplacian, Delta(1) (u) = div (Du/\Du\). (C) 2004 Published by Elsevier Ltd.