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An Imbedding

  1. Jul 11, 2013 #1
    Dear friends. I have a PDE to investigate its behavior at a semi-infinite cylinder. The nontrivial solution is considered to be in ##H^{2}(\Omega)\cap H_{0}^{1}(\Omega)##. Is it possible to say
    $$H^{2}(\Omega)\cap H_{0}^{1}(\Omega)\hookrightarrow H_{0}^{1}(\Omega)$$
    If the answer is positive, then the following estimate is possible:
    $$
    \int_{\Omega} \nabla u \nabla u_{t} dx < \frac {d}{2} \|\Delta u \|_{2}^{2}
    +\frac {1}{2} \|\nabla u_{t} \|_{2}^{2}
    $$
    where ##d## denotes the imbedding constant.
     
  2. jcsd
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