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Results tagged with sobolev-spaces
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user 151712
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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Orlicz–Sobolev spaces
if $n=1$,
\begin{eqnarray*}
\int^{+\infty}_1 \frac{\widehat{A_1}^{-1}(\tau)}{\tau^{1+\frac{1}{n}}}d\tau&=&\bigg[-n\tau^{-\frac{1}{n}}\widehat{A_1}^{-1}(\tau)\bigg]^{+\infty}_1\\
&+&n\int^{+\infty}_1\f …
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1
answer
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Orlicz–Sobolev spaces
Let $A$ be an N-function and suppose that
$$\int^{+\infty}_1\frac{A^{-1}(\tau)}{\tau^{1+\frac{1}{n}}}d\tau=+\infty. $$
We denote by $\widehat{A}$ an N-function equal to $A$ near infinity and $\widehat …