Vanishing exponent behavior for power curvature flow and applications

Date: 
2017/12/01 Fri 15:30 - 17:30
Room: 
Room 251, Building No.3
Speaker: 
Qing Liu
Affiliation: 
Fukuoka University
Abstract: 

In this talk, we discuss limit behavior for the power mean curvature flow equation as the exponent tends to zero. Such asymptotic behavior 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. The classical viscosity solution theory cannot be directly applied due to the jump discontinuity of the parabolic operator. We justify the convergence by modifying the definition of viscosity solutions to the limit equation and then establishing a comparison principle.