Quasiregular Families Bounded in Lp and Elliptic Estimates

Aimo Hinkkanen, Gaven Martin

Research output: Contribution to journalArticlepeer-review


We prove that a family F of quasiregular mappings of a domain Ω which are uniformly bounded in Lp for some p> 0 form a normal family. From this we show how an elliptic estimate on a functional difference implies all directional derivatives, and thus the complex gradient to be quasiregular. Consequently the function enjoys much higher regularity than apriori assumptions suggest. We present applications in the theory of Beltrami equations and their nonlinear counterparts.

Original languageEnglish (US)
Pages (from-to)1627-1636
Number of pages10
JournalJournal of Geometric Analysis
Issue number2
StatePublished - Apr 1 2020


  • Beltrami equations
  • Elliptic estimate
  • Nonlinear
  • Normal family
  • Quasiregular mappings

ASJC Scopus subject areas

  • Geometry and Topology


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