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On convergence rates for solutions of approximate mean curvature equations. (English) Zbl 1241.53057
Author’s abstract: L.C. Evans and J. Spruck [J. Differ. Geom. 33, No. 3, 635–681 (1991; Zbl 0726.53029)] considered an approximate equation for the level-set equation of the mean curvature flow and proved the convergence of solutions. K. Deckelnick [Interfaces Free Bound. 2, No. 2, 117–142 (2000; Zbl 0997.65112)] established a rate for the convergence. In this paper, we will provide a simple proof for the same result as that of Deckelnick. Moreover, we consider generalized mean curvature equations and introduce approximate equations for them and then establish a rate for the convergence.

MSC:
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35D40 Viscosity solutions to PDEs
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