Aleksandrov reflection and nonlinear evolution equations. I: The \(n\)-sphere and \(n\)-ball (Q1913318)
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scientific article; zbMATH DE number 881148
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Aleksandrov reflection and nonlinear evolution equations. I: The \(n\)-sphere and \(n\)-ball |
scientific article; zbMATH DE number 881148 |
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Aleksandrov reflection and nonlinear evolution equations. I: The \(n\)-sphere and \(n\)-ball (English)
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24 November 1996
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The authors consider fully nonlinear degenerate parabolic equations on the \(n\)-sphere \(S^n\). The problem corresponds to the evolution of a hypersurface in Euclidean space by a general function of the principal curvatures. Using Alexandrov reflection method a boundedness estimate on the gradient is proved. A generalization of the estimate to consider fully nonlinear degenerate parabolic equations on balls is also considered.
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\(n\)-ball
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parabolic equations
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\(n\)-sphere
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