Asymptotic behavior of solutions of the nonlinear Beltrami equation with the Jacobian

TL;DR

This paper studies how solutions to a nonlinear Beltrami equation behave at infinity, focusing on the Jacobian term, and demonstrates the bounds' sharpness through examples.

Contribution

It provides new insights into the asymptotic behavior of solutions to nonlinear Beltrami equations with Jacobian terms, including sharp bounds and illustrative examples.

Findings

Established asymptotic bounds for solutions at infinity.

Demonstrated the sharpness of bounds with examples.

Enhanced understanding of nonlinear Beltrami equations' solutions.

Abstract

We investigate the asymptotic behavior at infinity of regular homeomorphic solutions of the nonlinear Beltrami equation with the Jacobian on the right-hand side. The sharpness of the above bounds is illustrated by several examples.