AN OBSTACLE PROBLEM ARISING IN LARGE EXPONENT LIMIT OF POWER MEAN CURVATURE FLOW EQUATION

被引：2

作者：

Liu, Qing ^{[1
]}

Yamada, Naoki ^{[1
]}

机构：

[1] Fukuoka Univ, Dept Appl Math, Fukuoka, Fukuoka 8140180, Japan

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 372卷 / 03期

基金：

日本学术振兴会;

关键词：

Power mean curvature flow; viscosity solutions; asymptotic behavior; TUG-OF-WAR; DEGENERATE PARABOLIC EQUATIONS; VISCOSITY SOLUTIONS; LEVEL SETS; FAST/SLOW DIFFUSION; GAME INTERPRETATION; GENERALIZED MOTION; NEUMANN PROBLEM; CONVEXITY; HYPERSURFACES;

D O I：

10.1090/tran/7717

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：2103 / 2141

页数：39

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