naa a22 4500 510781470 CHVBK 20180411083249.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1007/s11854-013-0002-5 doi (NATIONALLICENCE)springer-10.1007/s11854-013-0002-5 Kalaj David Faculty of Natural Sciences and Mathematics, University of Montenegro, Dzordza Vasingtona b.b. 81000, Podgorica, Montenegro aut A priori estimate of gradient of a solution of a certain differential inequality and quasiconformal mappings [Elektronische Daten] [David Kalaj] We prove a global estimate for the gradient of the solution of the Poisson differential inequality |Δu(x)| ≤ a|Du(x)|2 + b, x ∈ B n , where a, b < ∞ and $$u|_{S^{n - 1} } \in C^{1,\alpha } (S^{n - 1} ,\mathbb{R}^m )$$ . If m = 1 and $$a \le (n + 1)/({\left| u \right|_\infty }4n\sqrt n )$$ , then |Du| is a priori bounded. This generalizes some similar results due to S. Bernstein [4] and E. Heinz [10] for the plane. An application of these results yields the main result, namely that a quasiconformal mapping of the unit ball onto a domain with C 2 smooth boundary satisfying the Poisson differential inequality is Lipschitz continuous. This extends some results of the author, Mateljević, and Pavlović from the complex plane to ℝ n . Hebrew University Magnes Press, 2013 Journal d'Analyse Mathématique The Hebrew University Magnes Press 119/1(2013-04-01), 63-88 0021-7670 119:1<63 2013 119 11854 https://doi.org/10.1007/s11854-013-0002-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0002-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kalaj David Faculty of Natural Sciences and Mathematics, University of Montenegro, Dzordza Vasingtona b.b. 81000, Podgorica, Montenegro aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique The Hebrew University Magnes Press 119/1(2013-04-01), 63-88 0021-7670 119:1<63 2013 119 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer