The behavior of the best Sobolev trace constant and extremals in thin domains
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2004
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Abstract
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).
For the special case p = q, this problem leads to an eigenvalue problem with a nonlinear boundary condition. We also study the convergence of the eigenvalues and eigenvectors in this case. (C) 2003 Elsevier Inc. All rights reserved.
For the special case p = q, this problem leads to an eigenvalue problem with a nonlinear boundary condition. We also study the convergence of the eigenvalues and eigenvectors in this case. (C) 2003 Elsevier Inc. All rights reserved.
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Sobolev trace constants, p-Laplacian, nonlinear boundary conditions, eigenvalue problems