# On A Class of Degenerate And Singular Monge-Amp\`ere Equations

## TL;DR

This paper proves existence, uniqueness, and regularity results for a class of degenerate and singular Monge-Ampère equations on convex domains, linking solution regularity to domain convexity.

## Contribution

It establishes the existence, uniqueness, and Hölder continuity of solutions for a new class of degenerate and singular Monge-Ampère equations, with a novel relation to domain convexity.

## Key findings

- Proved existence and uniqueness of solutions.
- Established Hölder continuity of solutions.
- Linked Hölder exponent to domain convexity.

## Abstract

In this paper we shall prove the existence, uniqueness and global H$\ddot{o}$lder continuity for the Dirichlet problem of a class of Monge-Amp\`ere type equations which may be degenerate and singular on the boundary of convex domains. We will establish a relation of the H$\ddot{o}$lder exponent for the solutions with the convexity for the domains.