Characterizations of the Sobolev space H1 on the boundary of a strongly Lipschitz domain in 3‐D
Year: 2025
Type: article
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.
Source: Mathematische Nachrichten
Author: Nathanael Skrepek
Institution: TU Bergakademie Freiberg
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,460
OpenAlex ID: W4408354453