Traces of differential forms on Lipschitz domains, the boundary De Rham complex, and Hodge decompositions Dorina MitreaMarius MitreaMei-Chi Shaw 46E3558J1035N1014F4035F05differential formsLipschitz domainsSobolev and Besov spacestracesextensionscohomology We study the extent to which classical trace and extension theorems for scalar-valued functions can be extended to differential forms of higher-degree. For maximum applicability, this is done in the context of Lipschitz subdomains of Riemannian manifolds, and on the scale of Besov and Triebel-Lizorkin spaces. A key ingredient in this regard is the boundary De Rham complex, which we consider in the geometric and analytic setting above. Applications to Hodge-decompositions and interpolation with constraints are also presented. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3338 10.1512/iumj.2008.57.3338 en Indiana Univ. Math. J. 57 (2008) 2061 - 2096 state-of-the-art mathematics http://iumj.org/access/