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A global compactness result for singular elliptic problems involving critical Sobolev exponent
Authors:Daomin Cao  Shuangjie Peng
Institution:Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People's Republic of China ; Department of Mathematics, Xiao Gan University, Xiao Gan, People's Republic of China -- and -- Institute of Applied Mathematics, AMSS., Chinese Academy of Sciences, Beijing 100080, People's Republic of China
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 $E_{\lambda,\epsilon}(u)=\frac{1}{2}\int_{\Omega}(\vert\nabla u\vert^{2}-\frac{\... ...^2}{\vert x\vert^2}-\epsilon u^2)-\frac{1}{2^*}\int_{\Omega} \vert u\vert^{2^*}$. We study the limit behaviour of $u_n$ and obtain a global compactness result.

Keywords:Palais-Smale sequence  compactness  Sobolev and Hardy critical exponents
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