Cardioid-Type Domains and Regularity of Homeomorphic Extensions
- Artikkeli I: Xu, Haiqing (2020). Weighted estimates for diffeomorphic extensions of homeomorphisms. Rendiconti Lincei: Matematica e Applicazioni, 31 (1), 151-189. DOI: 10.4171/RLM/884
- Artikkeli II: Xu, Haiqing (2020). Optimal Extensions of Conformal Mappings from the Unit Disk to Cardioid-Type Domains. Journal of Geometric Analysis, First Online. DOI: 10.1007/s12220-019-00340-x
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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 ...
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.
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 ...
Äkkinen, Tuomo; Guo, Changyu (Springer, 2017)In this paper, we consider mappings on uniform domains with exponentially integrable distortion whose Jacobian determinants are integrable. We show that such mappings can be extended to the boundary and moreover these ...