# Capillary surfaces arising in singular perturbation problems

## TL;DR

This paper proves Bernstein-type theorems for stationary points of the Alt-Caffarelli functional in two and three dimensions, advancing understanding of capillary surfaces in singular perturbation problems.

## Contribution

It introduces new Bernstein theorems for stationary points of the Alt-Caffarelli functional in low dimensions, linking capillary surfaces to singular perturbation analysis.

## Key findings

- Bernstein-type theorems established for $ ext{dim}=2,3$
- Characterization of stationary points as capillary surfaces
- Advancement in understanding singular perturbation problems

## Abstract

In this paper we prove Bernstein type theorems for a class of stationary points of the Alt-Caffarelli functional in $\mathbb R^2$ and $\mathbb R^3$.