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）

地点：致远楼101室

时间：2018年4月18日 10:00

摘要：

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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