Advances in Differential Equations

A stability property for the generalized mean curvature flow equation

F. Camilli

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.


Export citation