# A note on the Harnack inequality for elliptic equations in divergence form

## TL;DR

This paper highlights that the Harnack inequality, a fundamental result for elliptic equations, was implicitly contained in De Giorgi's 1957 work, clarifying its historical development.

## Contribution

It reveals that the Harnack inequality was implicitly present in De Giorgi's original proof, providing historical insight into elliptic equation theory.

## Key findings

- Harnack inequality was hidden in De Giorgi's 1957 work
- Clarifies the historical development of elliptic regularity theory
- Connects De Giorgi's work with Moser's results

## Abstract

In 1957, De Giorgi [3] proved the H\"{o}lder continuity for elliptic equations in divergence form and Moser [7] gave a new proof in 1960. Next year, Moser [8] obtained the Harnack inequality. In this note, we point out that the Harnack inequality was hidden in [3].