Geodesic
Singularities in L^p-quasidisks
Tadeusz Iwaniec1 ; Jani Onninen2 ; Zheng Zhu3
1Syracuse University, Department of Mathematics
2Syracuse University, Department of Mathematics, and University of Jyväskylä, Department of Mathematics and Statistics
3University of Jyväskylä, Department of Mathematics and Statistics
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 1053-1069
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We study planar domains with exemplary boundary singularities of the form of cusps. A natural question is how much elastic energy is needed to flatten these cusps; that is, to remove singularities. We give, in a connection of quasidisks, a sharp integrability condition for the distortion function to answer this question.  
Keywords: Cusp, mappings of integrable distortion, quasiconformal, quasidisk

Tadeusz Iwaniec  1   ; Jani Onninen  2   ; Zheng Zhu  3

1 Syracuse University, Department of Mathematics
2 Syracuse University, Department of Mathematics, and University of Jyväskylä, Department of Mathematics and Statistics
3 University of Jyväskylä, Department of Mathematics and Statistics 
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Tadeusz Iwaniec; Jani Onninen; Zheng Zhu. Singularities in L^p-quasidisks. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 1053-1069. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a25/