Harnack inequality for degenerate and singular elliptic equations with unbounded drift

TL;DR

This paper establishes a Harnack inequality for solutions to elliptic equations with unbounded drift, especially at points with large gradients, advancing understanding of degenerate and singular elliptic equations.

Contribution

It introduces a Harnack inequality applicable to elliptic equations with unbounded drift at points of large gradient, a novel extension in the field.

Findings

Proved Harnack inequality for solutions with unbounded drift

Extended classical results to degenerate and singular cases

Applicable at points of large gradient

Abstract

We prove a Harnack inequality for functions which, at points of large gradient, are solutions of elliptic equations with unbounded drift.