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• Approximation of W1,p Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian 

  Campbell, D.; Hencl, S.; Tengvall, Ville (Elsevier Inc., 2018)

  Let Ω ⊂ R n, n ≥ 4, be a domain and 1 ≤ p < [n/2], where [a] stands for the integer part of a. We construct a homeomorphism f ∈ W1,p((−1, 1)n, R n) such that Jf = det Df > 0 on a set of positive measure and Jf < 0 on a set ...

• Jacobian of weak limits of Sobolev homeomorphisms 

  Hencl, Stanislav; Onninen, Jani (Walter de Gruyter GmbH, 2018)

  Let Ω be a domain in Rn, where n=2,3. Suppose that a sequence of Sobolev homeomorphisms fk:Ω→Rn with positive Jacobian determinants, J(x,fk)>0, converges weakly in W1,p(Ω,Rn), for some p⩾1, to a mapping f. We show that ...

• Jacobian of weak limits of Sobolev homeomorphisms 

  Hencl, Stanislav; Onninen, Jani (Walter de Gruyter GmbH, 2018)

  Let Ω be a domain in Rn, where n=2,3. Suppose that a sequence of Sobolev homeomorphisms fk:Ω→Rn with positive Jacobian determinants, J(x,fk)>0, converges weakly in W1,p(Ω,Rn), for some p⩾1, to a mapping f. We show that ...

• Controlled diffeomorphic extension of homeomorphisms 

  Koskela, Pekka; Wang, Zhuang; Xu, Haiqing (Pergamon Press, 2018)

  Let Ω be an internal chord-arc Jordan domain and φ:S→∂Ω be a homeomorphism. We show that φ has finite dyadic energy if and only if φ has a diffeomorphic extension h:D→Ω which has finite energy.

• Weighted estimates for diffeomorphic extensions of homeomorphisms 

  Xu, Haiqing (European Mathematical Society Publishing House, 2020)

  Let Ω⊂R2Ω⊂R2 be an internal chord-arc domain and φ:S1→∂Ωφ:S1→∂Ω be a homeomorphism. Then there is a diffeomorphic extension h:D→Ωh:D→Ω of φφ. We study the relationship between weighted integrability of the derivatives of ...