On convergence rates for solutions of approximate mean curvature equations

Author:
Hiroyoshi Mitake

Journal:
Proc. Amer. Math. Soc. **139** (2011), 3691-3696

MSC (2010):
Primary 53C44, 65M15, 35D40

Published electronically:
March 30, 2011

MathSciNet review:
2813398

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Abstract | References | Similar Articles | Additional Information

Abstract: Evans and Spruck (1991) considered an approximate equation for the level-set equation of the mean curvature flow and proved the convergence of solutions. Deckelnick (2000) 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.

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Additional Information

**Hiroyoshi Mitake**

Affiliation:
Department of Applied Mathematics, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan

Email:
mitake@hiroshima-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-2011-11002-5

Keywords:
Mean curvature equation,
affine curvature equation,
approximate equations,
convergence rate

Received by editor(s):
August 25, 2010

Published electronically:
March 30, 2011

Additional Notes:
This work was partially supported by the Research Fellowship (22-1725) for Young Researcher from JSPS

Communicated by:
Matthew J. Gursky

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.