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• Dimension estimates for the boundary of planar Sobolev extension domains 

  Lučić, Danka; Rajala, Tapio; Takanen, Jyrki (Walter de Gruyter GmbH, 2023)

  We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev W1,pW1,p -extension domains via the weak mean porosity of the boundary. The sharpness of our estimate is ...

• Mappings of finite distortion : gauge dimension of generalized quasi-circles 

  Herron, D. A.; Koskela, Pekka (University of Illinois Press, 2003)

  We determine the correct dimension gauge for measuring generalized quasicircles (the images of a circle under so-called µ-homeomorphisms). We establish a sharp modulus of continuity estimate for the inverse of a homeomorphism ...

• Mappings of L p -integrable distortion: regularity of the inverse 

  Onninen, Jani; Tengvall, Ville (The RSE Scotland Foundation, 2016)

  Let X be an open set in R n and suppose that f : X → R n is a Sobolev homeomorphism. We study the regularity of f −1 under the L p -integrability assumption on the distortion function Kf . First, if X is the unit ...

• Sobolev homeomorphic extensions from two to three dimensions 

  Hencl, Stanislav; Koski, Aleksis; Onninen, Jani (Elsevier, 2024)

  We study the basic question of characterizing which boundary homeomorphisms of the unit sphere can be extended to a Sobolev homeomorphism of the interior in 3D space. While the planar variants of this problem are ...

• Two-Sided Boundary Points of Sobolev Extension Domains on Euclidean Spaces 

  García-Bravo, Miguel; Rajala, Tapio; Takanen, Jyrki (Springer, 2024)

  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 ...