# Approximation of the Helfrich's functional via Diffuse Interfaces

## TL;DR

This paper rigorously proves that Helfrich's functional, used in modeling biological membranes, can be approximated using diffuse interface methods under specific rigidity ratio constraints.

## Contribution

It provides a mathematical proof of the approximation of Helfrich's functional through diffuse interfaces, advancing theoretical understanding in membrane modeling.

## Key findings

- Established conditions for approximation validity
- Provided a rigorous mathematical proof
- Enhanced theoretical framework for membrane modeling

## Abstract

We give a rigorous proof of the approximability of the so-called Helfrich's functional via diffuse interfaces, under a constraint on the ratio between the bending rigidity and the Gauss-rigidity.