A global compactness result for singular elliptic problems involving critical Sobolev exponent

Cao, Daomin; Peng, Shuangjie

doi:10.1090/S0002-9939-02-06729-1

A global compactness result for singular elliptic problems involving critical Sobolev exponent
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by Daomin Cao and Shuangjie Peng PDF

Proc. Amer. Math. Soc. 131 (2003), 1857-1866 Request permission

Abstract:

Let $\Omega \subset R^N$ be a bounded domain such that $0 \in \Omega , N \geq 3,2^*=\frac {2N}{N-2},\lambda \in R, \epsilon \in R$. Let $\{u_n\}\subset H_0^1(\Omega )$ be a (P.S.) sequence of the functional $E_{\lambda ,\epsilon }(u)=\frac {1}{2}\int _{\Omega }(|\nabla u|^{2}-\frac {\lambda u^2}{|x|^2}-\epsilon u^2)-\frac {1}{2^*}\int _{\Omega } |u|^{2^*}$. We study the limit behaviour of $u_n$ and obtain a global compactness result.

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