Browsing by Author "Bonder, JF"

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    On the existence of extremals for the Sobolev trace embedding theorem with critical exponent
    (WILEY, 2005) Bonder, JF; Rossi, JD
    In this paper, the existence problem is studied for extremals of the Sobolev trace inequality W-1,W-p(Omega) --> L-p* (partial derivativeOmega), where Omega is a bounded smooth domain in R-N, p(*) = p(N - 1)/(N - p) is the critical Sobolev exponent, and 1 < p < N.
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    The behavior of the best Sobolev trace constant and extremals in thin domains
    (2004) Bonder, JF; Martínez, S; Rossi, JD
    In this paper, we study the asymptotic behavior of the best Sobolev trace constant and extremals for the immersion W-1,W-p (Omega) hooked right arrow L-q (partial derivativeOmega) in a bounded smooth domain when it is contracted in one direction. We find that the limit problem, when rescaled in a suitable way, is a Sobolev-type immersion in weighted spaces over a projection of Omega, W-1,W-p (P(Omega),alpha) hooked right arrow L-q (P(Omega), beta).