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(adsbygoogle = window.adsbygoogle || []).push({});

$$H^{2}(\Omega)\cap H_{0}^{1}(\Omega)\hookrightarrow H_{0}^{1}(\Omega)$$

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.

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# An Imbedding

Can you offer guidance or do you also need help?

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