An obstacle problem arising in large exponent limit of power mean curvature flow equation

Liu, Qing; Yamada, Naoki

doi:10.1090/tran/7717

An obstacle problem arising in large exponent limit of power mean curvature flow equation
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by Qing Liu and Naoki Yamada PDF

Trans. Amer. Math. Soc. 372 (2019), 2103-2141 Request permission

Abstract:

We study limit behavior for the level-set power mean curvature flow equation as the exponent tends to infinity. Under Lipschitz continuity, quasiconvexity, and coercivity of the initial condition, we show that the limit of the viscosity solutions can be characterized as the minimal supersolution of an obstacle problem involving the $1$-Laplacian. Such behavior is closely related to applications of power mean curvature flow in image denoising. We also discuss analogous behavior for other evolution equations with related applications.

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