Abstract
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 language | English (US) |
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Pages (from-to) | 1627-1636 |
Number of pages | 10 |
Journal | Journal of Geometric Analysis |
Volume | 30 |
Issue number | 2 |
DOIs | |
State | Published - Apr 1 2020 |
Keywords
- Beltrami equations
- Elliptic estimate
- Nonlinear
- Normal family
- Quasiregular mappings
ASJC Scopus subject areas
- Geometry and Topology