Aleksandrov reflection and nonlinear evolution equations. I: The \(n\)-sphere and \(n\)-ball
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.
scientific article; zbMATH DE number 881148