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Results tagged with sobolev-spaces
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user 320386
A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.
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Reference for proof about a result concerning Sobolev spaces and exponential growth
I'm reading an article and I saw the following affirmation without proof:
Let $u \in H^1(\mathbb{R}^2)$ and $\alpha>0$, then
$$\int_{\mathbb{R}^2}(e^{\alpha u^2}-1)dx<+\infty.$$
Is this claim really t …
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