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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: 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: http://dx.doi.org/10.1090/S0002-9939-2011-11002-5
PII: S 0002-9939(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.