Lipschitz domains, domains with corners and the Hodge Laplacian

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72329We define self-adjoint extensions of the Hodge Laplacian on Lipschitz domains in Riemannian manifolds, corresponding to either the absolute or the relative boundary condition, and examine regularity properties of these operators' domains and form domains. We obtain results valid for general Lipschitz domains, and stronger results for a special class of ``almost convex'' domains, which apply to domains with corners.20 pages; amstexAnalysis of PDEsDifferential Geometry31C12, 35B65, 35J25 (Primary) 58J32, 42B20 (Secondary)Lipschitz domains, domains with corners and the Hodge Laplaciantext