Boundary regularity on the parabolic Monge-Ampère equation
type: Item
instance of: scholarly article
title: Boundary regularity on the parabolic Monge-Ampère equation
zbMATH Open document ID: 1333.35127
author: Lin Tang
published in: Journal of Differential Equations
publication date: 2015-09-22T00:00:00Z
review text: 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)].
reviewed by: Stephan Fackler
Mathematics Subject Classification ID: 35K96
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35D40
zbMATH DE Number: 6484242
zbMATH Keywords: boundary regularity
zbMATH Keywords: Hölder estimates
zbMATH Keywords: parabolic Monge-Ampère equation
MaRDI profile type: Publication
full work available at URL: j.jde.2015.07.026
OpenAlex ID: W1195562168
cites work: Gauss curvature flow: The fate of the rolling stones
cites work: Interior a priori estimates for solutions of fully nonlinear equations
cites work: Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
cites work: The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
cites work: The Monge-Ampère equation
cites work: Geometric properties of the sections of solutions to the Monge-Ampère equation
cites work: A generalization of a theorem by Calabi to the parabolic Monge-Ampere equation
cites work: \(W^{2,p}\) estimates for the parabolic Monge-Ampère equation
cites work: Harnack inequality for the linearized parabolic Monge-Ampère equation
cites work: On a priori C 1, α and W 2, p estimates for a parabolic Monge-Ampere equation in the Gauss curvature flows
cites work: Sequences of convex functions and estimates of the maximum of the solution of a parabolic equation
cites work: Q5562267
cites work: Q4354424
cites work: Pointwise 𝐶^{2,𝛼} estimates at the boundary for the Monge-Ampère equation
cites work: Global \(W^{2,p}\) estimates for the Monge-Ampère equation
cites work: Regularity results on the parabolic Monge-Ampère equation with \(VMO\) type data
cites work: Deforming a hypersurface by its Gauss-Kronecker curvature
cites work: Boundary regularity for the Monge-Ampère and affine maximal surface equations
cites work: On an Aleksandrov-Bakel'Man Type Maximum Principle for Second-Order Parabolic Equations
cites work: Q4229039
cites work: On the regularity theory of fully nonlinear parabolic equations: I
cites work: On the regularity theory of fully nonlinear parabolic equations: II
cites work: Q4696906
cites work: An improvement of a result of Ivochkina and Ladyzhenskaya on a type of parabolic Monge-Ampère equation
DOI: 10.1016/J.JDE.2015.07.026
description: scientific article; zbMATH DE number 6484242