# Elliptic regularization of the isometric immersion problem

## TL;DR

This paper introduces a geometric elliptic regularization for the PDE system governing the isometric immersion of surfaces in three-dimensional space, providing a new approach with a natural variational interpretation.

## Contribution

It presents a novel elliptic regularization method for the isometric immersion problem, enhancing the mathematical framework with geometric and variational insights.

## Key findings

- Regularization makes the PDE system elliptic
- Provides a variational interpretation of the regularization
- Potentially improves solvability and analysis of the immersion problem

## Abstract

We introduce an elliptic regularization of the PDE system representing the isometric immersion of a surface in $\mathbb R^{3}$. The regularization is geometric, and has a natural variational interpretation.