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Smoothness of the billiard ball map for strictly convex domains near the boundary


Author: Valery Kovachev
Journal: Proc. Amer. Math. Soc. 103 (1988), 856-860
MSC: Primary 58F11; Secondary 58F10
DOI: https://doi.org/10.1090/S0002-9939-1988-0947670-1
MathSciNet review: 947670
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Abstract: The billiard ball map in bounded strictly convex domains in $ {{\mathbf{R}}^n}$ with boundaries of class $ {C^k},k \geq 2$, is considered and its smoothness of class $ {C^{k - 1}}$ up to the boundary is proved.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0947670-1
Keywords: Smoothness near the boundary, billiard, convex
Article copyright: © Copyright 1988 American Mathematical Society

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