## Advances in Differential Equations

- Adv. Differential Equations
- Volume 3, Number 6 (1998), 815-846.

### A stability property for the generalized mean curvature flow equation

#### Abstract

In this paper we will study stability properties for viscosity solutions of geometric equations. We will prove that, if the interface is regular (i.e., it is the boundary of an open set and it is not fat), the signed distance function from the front is stable for geometric perturbations of the equation. This result is based on representation formulas for viscosity solutions in terms of distance functions from the level sets. An application of the previous result to stability of approximation schemes is also presented.

#### Article information

**Source**

Adv. Differential Equations, Volume 3, Number 6 (1998), 815-846.

**Dates**

First available in Project Euclid: 18 April 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1366292550

**Mathematical Reviews number (MathSciNet)**

MR1659277

**Zentralblatt MATH identifier**

0957.35072

**Subjects**

Primary: 35K55: Nonlinear parabolic equations

Secondary: 35B35: Stability 49L25: Viscosity solutions 58E15: Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.

#### Citation

Camilli, F. A stability property for the generalized mean curvature flow equation. Adv. Differential Equations 3 (1998), no. 6, 815--846. https://projecteuclid.org/euclid.ade/1366292550