Mathematics – Analysis of PDEs
Scientific paper
2010-04-21
Mathematics
Analysis of PDEs
Scientific paper
We consider the nonlinear and nonlocal problem $$ A_{1/2}u=|u|^{2^\sharp-2}u\ \text{in \Omega, \quad u=0 \text{on} \partial\Omega $$where $A_{1/2}$ represents the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions, $\Omega$ is a bounded smooth domain in $\R^n$, $n\ge 2$ and $2^{\sharp}=2n/(n-1)$ is the critical trace-Sobolev exponent. We assume that $\Omega$ is annular-shaped, i.e., there exist $R_2>R_1>0$ constants such that $\{x\in\R^n\ \text{= s.t.}\ R_1<|x|
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