2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162980For 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 $R^n$.94 pagesFunctional Analysis46E35Sobolev $W^1_p$-spaces on closed subsets of $R^n$text