Characterizations of the Sobolev space H¹ on the boundary of a strongly Lipschitz domain in 3‐D

Abstract In this work, we investigate the Sobolev space on a strongly Lipschitz boundary , that is, is a strongly Lipschitz domain (not necessarily bounded). In most of the literature, this space is defined via charts and Sobolev spaces on flat domains. We show that there is a different approach via differential operators on and a weak formulation directly on the boundary that leads to the same space. This second characterization of is in particular of advantage, when it comes to traces of vector fields.