Sobolev Lp2-functions on closed subsets of R2

For each p>2 we give intrinsic characterizations of the restriction of the homogeneous Sobolev space Lp2(R2) to an arbitrary finite subset E of R2. 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.