Geodesic
Singularities in L^p-quasidisks
Tadeusz Iwaniec1 ; Jani Onninen2 ; Zheng Zhu3
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
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/