Differential and Integral Equations

Some regularity results for anisotropic motion of fronts

Cyril Imbert

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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

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

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B25: Singular perturbations
Secondary: 35B65: Smoothness and regularity of solutions 35J60: Nonlinear elliptic equations 35K55: Nonlinear parabolic equations 35R35: Free boundary problems 49L25: Viscosity solutions


Imbert, Cyril. Some regularity results for anisotropic motion of fronts. Differential Integral Equations 15 (2002), no. 10, 1263--1271. https://projecteuclid.org/euclid.die/1356060754

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