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Interfaces and Free Boundaries

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Volume 22, Issue 1, 2020, pp. 51–84
DOI: 10.4171/IFB/432

Published online: 2020-04-15

The vanishing exponent limit for motion by a power of mean curvature

Qing Liu[1]

(1) Fukuoka University, Japan

We discuss limit behavior of solutions to level set equation of power mean curvature flow as the exponent tends to zero, which has important applications to shape analysis in image processing. A formal limit yields a fully nonlinear singular equation that describes the motion of a surface by the sign of its mean curvature.We justify the convergence by providing a definition of viscosity solutions to the limit equation and establishing a comparison principle.

Keywords: Power mean curvature flow, viscosity solutions, asymptotic behavior, discontinuous parabolic equation

Liu Qing: The vanishing exponent limit for motion by a power of mean curvature. Interfaces Free Bound. 22 (2020), 51-84. doi: 10.4171/IFB/432