Boundary regularity on the parabolic Monge-Ampère equation
The author proves Hölder estimates up to the boundary on bounded convex Lipschitz domains of viscosity solutions of the parabolic Monge-Ampère equation \[ -u_t + (\operatorname{det} D^2 u)^{1/n} = f, \] assuming that the solutions are convex in the spatial variables. Furthermore, if the domain is assumed to be \(C^2\), then Hölder estimates on the first derivatives and \(L^p\)-estimates on the second derivatives are obtained as well. The results partially generalize interior estimates proved in [\textit{Q. Huang} and \textit{G. Lu}, Am. J. Math. 128, No. 2, 453--480 (2006; Zbl 1098.35078)].
scientific article; zbMATH DE number 6484242
scientific article