Two-sided boundary points of Sobolev-extension domains on Euclidean spaces

2021/11/01 by Miguel García‐Bravo, García-Bravo, Miguel, Tapio Rajala +3
Computer Science · Mathematics · #28A75 #46E35 #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2111.01079

openalex publication_date 2021/11/01 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We prove an estimate on the Hausdorff-dimension of the set of two-sided boundary points of general Sobolev-extension domains on Euclidean spaces. We also present examples showing lower bounds on possible dimension estimates of this type.

Related

• Dimension estimate for the two-sided points of planar Sobolev extension domains
• Dimension estimates for the boundary of planar Sobolev extension domains
• A necessary condition for Sobolev extension domains in higher dimensions
• On planar Sobolev L^m_p-extension domains
• Bounding the Dimension of Points on a Line