Sobolev $L^2_p$-functions on closed subsets of $R^2$

Pavel Shvartsman

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arXiv · 1210.0590

Sobolev $L^2_p$-functions on closed subsets of $R^2$

Pavel Shvartsman

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Abstract

For each $p>2$ we give intrinsic characterizations of the restriction of the homogeneous Sobolev space $L^1_p(R^2)$ to an arbitrary finite subset $E$ of $R^2$. The trace criterion is expressed in terms of certain weighted oscillations of the second order with respect to a measure generated by the Menger curvature of triangles with vertices in $E$.

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BibTeX RIS

Pavel Shvartsman. 2012-10-01. Sobolev $L^2_p$-functions on closed subsets of $R^2$. https://arxiv.org/abs/1210.0590

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