Bi-Lipschitz invariance of planar BV- and W^1,1-extension domains

2021/06/14 by Miguel García‐Bravo, García-Bravo, Miguel, Tapio Rajala +3
Mathematics · #46E35 #Algebraic Geometry and Number Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2106.07330

openalex publication_date 2021/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a bi-Lipschitz image of a planar BV-extension domain is also a BV-extension domain, and that a bi-Lipschitz image of a planar W^1,1-extension domain is again a W^1,1-extension domain.

Citations

• Sobolev embeddings, extensions and measure density condition

Related

• Planar W^{1, 1}-extension domains
• Strong BV-extension and W^1,1-extension domains
• The extension property for domains with one singular point
• A planar bi-Lipschitz extension Theorem
• A geometric characterization of planar Sobolev extension domains