Title: Traces of differential forms on Lipschitz domains, the boundary De Rham complex, and Hodge decompositions

Authors: Dorina Mitrea, Marius Mitrea and Mei-Chi Shaw

Issue: Volume 57 (2008), Issue 5, 2061-2096

Abstract: 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.