2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172606We consider the heat equation with Dirichlet boundary conditions on the tubular neighborhood of a closed Riemannian submanifold. We show that, as the tube diameter tends to zero, a suitably rescaled and renormalized semigroup converges to a limit semigroup in Sobolev spaces of arbitrarily large Sobolev index.30 pagesAnalysis of PDEsProbability35K05 (Primary); 74Q10 (Secondary)text