The Growth of Gradients for Solutions to certain Laplacian-Gradient Inequalities and general Poisson's equations in n-dimensional Euclidean space

Abstract

Here we review M. Mateljević’s article [9], with some novelities. We focus on mappings between smooth domains which have bounded Laplacian. As an application, if these mappings are quasiconformal, we obtain some results on the behavior of their partial derivatives on the boundary. In the last part of this article, we announce one new result of the author of [9], which has been recently presented on Belgrade Seminary of Complex Analysis.