Sobolev $W^1_p$-spaces on closed subsets of $R^n$

Mathematics – Functional Analysis

Scientific paper

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94 pages

Scientific paper

For each $p>n$ we use local oscillations and doubling measures to give
intrinsic characterizations of the restriction of the Sobolev space
$W_p^1(R^n)$ to an arbitrary closed subset of $R^n$.

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