Singularities in L^p-quasidisks

Authors

  • Tadeusz Iwaniec Syracuse University, Department of Mathematics
  • Jani Onninen Syracuse University, Department of Mathematics, and University of Jyväskylä, Department of Mathematics and Statistics
  • Zheng Zhu University of Jyväskylä, Department of Mathematics and Statistics

Keywords:

Cusp, mappings of integrable distortion, quasiconformal, quasidisk

Abstract

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.

 

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Published

2021-08-30

Issue

Vol. 46 No. 2 (2021)

Section

Articles

License

Copyright (c) 2021 The Finnish Mathematical Society

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Iwaniec, T., Onninen, J., & Zhu, Z. (2021). Singularities in L^p-quasidisks. Annales Fennici Mathematici, 46(2), 1053-1069. https://afm.journal.fi/article/view/111044