Lipschitz domains, domains with corners and the Hodge Laplacian

Mitrea, Marius; Taylor, Michael; Vasy, Andras

Lipschitz domains, domains with corners and the Hodge Laplacian

Authors

Mitrea, Marius

Taylor, Michael

Vasy, Andras

Description

We 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; amstex