# The Dirichlet problem for fully nonlinear degenerate elliptic equations with a singular nonlinearity

## TL;DR

This paper studies the Dirichlet problem for a broad class of degenerate elliptic equations with singular terms, establishing conditions for existence and uniqueness of positive viscosity solutions in convex domains.

## Contribution

It provides new sharp existence and uniqueness results for positive viscosity solutions of degenerate elliptic equations with singular nonlinearities.

## Key findings

- Established sharp existence results for positive solutions.
- Proved uniqueness of solutions under certain conditions.
- Extended the theory to include degenerate elliptic equations with singular terms.

## Abstract

We investigate the homogeneous Dirichlet problem in uniformly convex domains for a large class of degenerate elliptic equations with singular zero order term. In particular we establish sharp existence and uniqueness results of positive viscosity solutions.