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• Planar Sobolev extension domains 

  Zhang, Yi (University of Jyväskylä, 2017)

  This doctoral thesis deals with geometric characterizations of bounded planar simply connected Sobolev extension domains. It consists of three papers. In the first and third papers we give full geometric characterizations ...

• 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 ...

• Sobolev homeomorphic extensions onto John domains 

  Koskela, Pekka; Koski, Aleksis; Onninen, Jani (Elsevier Inc., 2020)

  Given the planar unit disk as the source and a Jordan domain as the target, we study the problem of extending a given boundary homeomorphism as a Sobolev homeomorphism. For general targets, this Sobolev variant of the ...

• Dimension estimate for the two-sided points of planar Sobolev extension domains 

  Takanen, Jyrki (American Mathematical Society (AMS), 2023)

  In this paper we give an estimate for the Hausdorff dimension of the set of two-sided points of the boundary of bounded simply connected Sobolev W1,p-extension domain for 1 < p < 2. Sharpness of the estimate is shown by ...

• The volume of the boundary of a Sobolev (p,q)-extension domain 

  Koskela, Pekka; Ukhlov, Alexander; Zhu, Zheng (Elsevier, 2022)

  Let n≥2 and $1\leq q<p><\fz$. We prove that if Ω⊂Rn is a Sobolev (p,q)-extension domain, with additional capacitory restrictions on boundary in the case q≤n−1, n>2, then |∂Ω|=0. In the case 1≤q0.</p>