SINGULARITIES IN ℒp-QUASIDISKS

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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.

Original languageEnglish (US)
Pages (from-to)1053-1069
Number of pages17
JournalAnnales Fennici Mathematici
Volume46
Issue number2
DOIs
StatePublished - 2021

Keywords

  • Cusp
  • Mappings of integrable distortion
  • Quasiconformal
  • Quasidisk

ASJC Scopus subject areas

  • Mathematics(all)

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