Extension Operators for Fractional Sobolev Spaces on Lipschitz Submanifolds
Published in arXiv, 2025
Recommended citation: Weder, P., 2025. Extension Operators for Fractional Sobolev Spaces on Lipschitz Submanifolds. https://doi.org/10.48550/arXiv.2507.04869 https://arxiv.org/abs/2507.04869
A well-known result is that any Lipschitz domain is an extension domain for Ws,p. This paper extends this result to Lipschitz subsets of compact Lipschitz submanifolds of ℝn. We adapt the construction of an extension operator for Lipschitz domains in arXiv:1104.4345v3 to manifolds via local coordinate charts. Furthermore, the dependence on the size of the extension domain is explicit in all estimates. This result is motivated by applications in numerical analysis, most notably geometry simplification, where the explicit dependence of the continuity constant on the domain size is essential.