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

Pavel Shvartsman

paper

Sobolev $L_{p}^{2}$ -functions on closed subsets of $R^{2}$

arXiv:1210.0590

Abstract

For each $p > 2$ we give intrinsic characterizations of the restriction of the homogeneous Sobolev space $L_{p}^{1} (R^{2})$ 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 $E$ .

109 pages

Sobolev Lp2​-functions on closed subsets of R2

Abstract

References in corpus (2)

Sobolev $L_{p}^{2}$ -functions on closed subsets of $R^{2}$