## Differential and Integral Equations

### Some regularity results for anisotropic motion of fronts

Cyril Imbert

#### Abstract

We study the regularity of propagating fronts whose motion is anisotropic. We prove that there is at most one normal direction at each point of the front; as an application, we prove that convex fronts are $C^{1,1}.$ These results are by-products of some necessary conditions for viscosity solutions of quasilinear elliptic equations. These conditions are of independent interest; for instance they imply some regularity for viscosity solutions of nondegenerate quasilinear elliptic equations.

#### Article information

Source
Differential Integral Equations, Volume 15, Number 10 (2002), 1263-1271.

Dates
First available in Project Euclid: 21 December 2012