Extension Operators for Fractional Sobolev Spaces on Lipschitz Submanifolds

2025/07/07 by Philipp Weder, Weder, Philipp · 1 citation
Mathematics · #35R01 #46E35 #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2507.04869

openalex publication_date 2025/07/07 · openalex created_date 2025/10/20 · openalex updated_date 2026/07/28

Abstract

A well-known result is that any Lipschitz domain is an extension domain for W^s,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.

Citations

• An Eulerian Finite Element Method for PDEs in time-dependent domains
• Hitchhiker's guide to the fractional Sobolev spaces
• Hitchhikerʼs guide to the fractional Sobolev spaces

Cited by

• Analysis-Aware Defeaturing of Dirichlet Features

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