On convergence rates for solutions of approximate mean curvature equations
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- by Hiroyoshi Mitake PDF
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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.References
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Additional Information
- Hiroyoshi Mitake
- Affiliation: Department of Applied Mathematics, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan
- MR Author ID: 824759
- Email: mitake@hiroshima-u.ac.jp
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 3691-3696
- MSC (2010): Primary 53C44, 65M15, 35D40
- DOI: https://doi.org/10.1090/S0002-9939-2011-11002-5
- MathSciNet review: 2813398