Conformal Structure of Autonomous Leray-Lions Equations in the Plane and Linearisation by Hodograph Transform

TL;DR

This paper establishes conditions under which autonomous elliptic Leray-Lions equations in the plane possess a conformal structure, enabling their linearisation via the hodograph transform, thus advancing the understanding of their geometric properties.

Contribution

The paper identifies sufficient conditions for conformal structure in autonomous elliptic Leray-Lions equations and demonstrates their linearisation through the hodograph transform.

Findings

Conformal structure exists under specific conditions for these equations.

Linearisation achieved via hodograph transform.

Provides geometric insight into Leray-Lions equations.

Abstract

We give sufficient conditions for when an autonomous elliptic Leray-Lions equation in the plane has a conformal structure. This allows the Leray-Lions equation to be linearised in a special form through the hodograph transform.