Annales Academię Scientiarum Fennicę
Mathematica
Volumen 36, 2011, 177-194
University of Montenegro, Faculty of Natural Sciences and
Mathematics
Cetinjski put b.b. 81000 Podgorica, Montenegro; davidk 'at' t-com.me
Abstract. It is proved that the family of K quasiconformal mappings of the unit ball onto itself satisfying PDE \Delta u = g, g \in L\infty(Bn), u(0) = 0, is a uniformly Lipschitz family. In addition, it is showed that the Lipschitz constant tends to 1 as K \to 1 and |g|\infty \to 0. This generalizes a similar two-dimensional case treated in [21] and solves the problem initialized in [16].
2000 Mathematics Subject Classification: Primary 30C65; Secondary 31B05.
Key words: Quasiconformal maps, PDE, Lipschitz condition.
Reference to this article: D. Kalaj: On the quasiconformal self-mappings of the unit ball satisfying the Poisson differential equation. Ann. Acad. Sci. Fenn. Math. 36 (2011), 177-194.
doi:10.5186/aasfm.2011.3611
Copyright © 2011 by Academia Scientiarum Fennica