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$C^{2,\alpha }$ estimate of a parabolic Monge-Ampère equation on $S^{n}$

Author(s): Dong-Ho Tsai
Journal: Proc. Amer. Math. Soc. 131 (2003), 3067-3074.
MSC (2000): Primary 35K10, 58J35
Posted: February 6, 2003
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Abstract: We consider a special type of parabolic Monge-Ampère equation on $S^{n}$arising from convex hypersurfaces expansion in Euclidean spaces. We obtained a $C^{2,\alpha }$ parabolic estimate of the support functions for the convex hypersurfaces assuming that we have already had a $C^{2}$parabolic estimate.

References:

[AN]
B. Andrews,Motion of hypersurfaces by Gauss curvature, Pacific J. of Math., 195 (2000) 1-34. MR 2001i:53108

[CA]
L. Caffarelli, Interior $W^{2,p}$estimates for solutions of the Monge-Ampére equation, Annals of Math., 131 (1990) 135-150. MR 91f:35059

[C]
B. Chow, Geometric aspects of Aleksandrov reflection and gradient estimates for parabolic equations, Comm. Anal. Geom., Vol. 5, Num. 2 (1997) 389-409. MR 98k:53045

[CG]
B. Chow, R. Gulliver, Aleksandrov reflection and nonlinear evolution equations, I: The ${n}$-sphere and $n$-ball, Calculus of Variation, 4 (1996) 249-264. MR 97f:53064

[CT]
B. Chow, D. H. Tsai, Nonhomogeneous Gauss curvature flows, Indiana Univ. Math. J., 47 (1998) 965-994. MR 2000a:53116

[KS]
N. V. Krylov, M. V. Safonov, Certain properties of parabolic equations with measurable coefficients, Izv. Akad. Nauk SSSR Ser. Mat., 40 (1980) 161-175; English transl., Math. USSR Izv., 16 (1981) 151-164. MR 83c:35059

[LSU]
O. A. Ladyzenskaya, V. A. Solonikov, N. N. Ural´ceva, Linear and Quasilinear Equations of Parabolic Type, Translations of Math. Mono., V. 23, AMS. MR 39:3159b

[T]
K. Tso, Deforming a hypersurface by its Gauss-Kronecker curvature, Comm. Pure and Appl. Math., 38 (1985) 867-882. MR 87e:53009

[U]
J. Urbas, An expansion of convex hypersurfaces, J. Diff. Geom., 33 (1991) 91-125; Correction to, ibid., 35 (1992) 763-765. MR 93b:58142

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Additional Information:

Dong-Ho Tsai
Affiliation: Department of Mathematics, National Tsing Hua University, Hsinchu 300, Taiwan
Email: dhtsai@math.nthu.edu.tw

DOI: 10.1090/S0002-9939-03-06848-5
PII: S 0002-9939(03)06848-5
Received by editor(s): August 2, 2001
Received by editor(s) in revised form: April 23, 2002
Posted: February 6, 2003
Additional Notes: This research was supported by NSC of Taiwan, Grant # 89-2115-M-194-026
Communicated by: Bennett Chow
Copyright of article: Copyright 2003, American Mathematical Society

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