Removability of product sets for Sobolev functions in the plane

2021/11/05 by Tapio Rajala, Rajala, Tapio, Ugo Bindini +1 · 1 citation
Mathematics · #45E35 #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2111.03381

openalex publication_date 2021/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study conditions on closed sets C,F ⊂ ℝ making the product C × F removable or non-removable for W^1,p. The main results show that the Hausdorff-dimension of the smaller dimensional component C determines a critical exponent above which the product is removable for some positive measure sets F, but below which the product is not removable for another collection of positive measure totally disconnected sets F. Moreover, if the set C is Ahlfors-regular, the above removability holds for any totally disconnected F.

Cited by

• On Removable Sets for Weighted Sobolev Functions

Related

• Removable sets for Orlicz-Sobolev spaces
• On Removable Sets for Weighted Sobolev Functions
• Removability of exceptional sets for differentiable and Lipschitz functions
• On Removable Sets For Convex Functions
• Hausdorff dimension of removable sets for elliptic and canceling homogeneous differential operators in the class of bounded functions