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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 ...

• A density result on Orlicz-Sobolev spaces in the plane 

  Ortiz, Walter A.; Rajala, Tapio (Elsevier, 2021)

  We show the density of smooth Sobolev functions Wk,∞(Ω)∩C∞(Ω) in the Orlicz-Sobolev spaces Lk,Ψ(Ω) for bounded simply connected planar domains Ω and doubling Young functions Ψ.

• Classical flows of vector fields with exponential or sub-exponential summability 

  Ambrosio, Luigi; Nicolussi Golo, Sebastiano; Serra Cassano, Francesco (Elsevier BV, 2023)

  We show that vector fields b whose spatial derivative Dx b satisfies a Orlicz summability condition have a spatially continuous representative and are well-posed. For the case of sub-exponential summability, their flows ...

• 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 ...