题目：On Small and Large Exponent Limits of Power Mean Curvature Flow Equation
报告人：柳青 （福冈大学 助理教授）
Motivated by applications in image processing, we study asymptotic behavior for the level set equation of power mean curvature flow as the exponent tends to 0 or to infinity. When the exponent is vanishing, we formally obtain 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. In the large exponent case, the limit equation can be characterized as a stationary obstacle problem involving 1-Laplacian when the initial value is assumed to be convex.
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