A comparison result for radial solutions of the mean curvature equation

TL;DR

This paper presents comparison results for radial solutions of the mean curvature equation, relating them to circular arcs with the same boundary conditions, and demonstrates applications including physically motivated examples.

Contribution

It introduces new comparison theorems for mean curvature solutions and applies them to various practical examples with physical relevance.

Findings

Comparison results between mean curvature solutions and circular arcs.

Applications to physically motivated problems.

Examples demonstrating the effectiveness of the estimates.

Abstract

We establish two comparison results between the solutions of a class of mean curvature equations and pieces of arcs of circles that satisfy the same Neumann boundary condition. Finally we present a number of examples where our estimates can be applied, some of them have a physical motivation.