# The role of the Hilbert metric in a class of singular elliptic boundary value problem in convex domains

## TL;DR

This paper explores how the Hilbert metric influences the analysis of existence and uniqueness of solutions to a class of singular elliptic boundary-value problems in convex domains.

## Contribution

It demonstrates the key role of the Hilbert metric in establishing solution properties for singular elliptic boundary-value problems.

## Key findings

- Hilbert metric is equivalent to Thompson metric in convex domains.
- The metric aids in proving existence and uniqueness of solutions.
- Application to boundary-value problems with boundary singularities.

## Abstract

In a recent paper [7], we were led to consider a distance over a bounded open convex domain. It turns out to be the so-called Thompson metric, which is equivalent to the Hilbert metric. It plays a key role in the analysis of existence and uniqueness of solutions to a class of elliptic boundary-value problems that are singular at the boundary.