  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 $E$.
