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Results tagged with extension
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user 483492
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$H^1 \cap C^0$ boundary, smooth $H^1$ extension
Now the question is, does there exist a $C^\infty$ extension $\tilde{u}$ to some $\tilde{\Omega} \supset \Omega$ such that $\tilde{u} \in H^1(\tilde{\Omega}; \mathbb{R}^n)$? … Note:
We always get a smooth extension, but if it would remain in $H^1$ is the hard part. …
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